Surely we could make anything that the aliens described even if we didn't understand how it worked. Or can we imagine something that we can't possibly make, given modern technology and manufacturing knowledge?

Yes, we can. Some things that come to mind:

• it requires some really exotic material (say, heavy transuranics or dark matter). The aliens also have methods to locate or manufacture those, but we don't. So, we need to first build the machines that will build the machines that will build the machines...


• it requires much tighter tolerances - say, one-nanometer etching capability. We still don't have that (not at any industrially significant level, at least). Aliens have machines that do this, but they also require the same capability, much as modern chip factories require chips to work.

In both cases, we wouldn't need or be able to use the alien's XXVth century technology: we would need their 22nd century technology to be able to build their 23rd century machines that will enable us to build 24th century technology that will finally be able to use and build alien-current technology.

You say we now have "everything" - from electron microscopes to X-ray beams. We do have those, but how do we know they're "everything"? Maybe the aliens discovered micro-gravitics and are now based on that.

The belief that we had "everything" has already been declared "two or three times" in human history, and every time it turned out we were wrong.

other possibilities: abhorrent technology

The required raw materials could include something that can't be easily duplicated or harvested, such as the brain matter of a healthy, full-grown adult of the species. In essence, human sacrifice.

While this wouldn't be anything difficult for, say, an ant colony, or a hive mind (or even a technologically advanced Aztec nation), it would be regarded as abhorrent and forbidden by most human governments, and publicly denounced by all.

I have no real alien technology schematics at hand.

The closest thing I can think of is the schematics of something it is not manufactured in the factory of my employer. Let's say it is the latest smartphone of a top notch brand.

On those schematics I would see which parts I need and how to assemble them. Good so far.

However, if I don't have access to the parts, I won't be able to assemble anything. I might have the raw silicon used to manufacture the microchips, but I will have no clue on what to etch in that chip.

Even worse, the schematics do not include the software controlling how the parts interact together, unless the assembly is a purely mechanical one. The software is often the razor splitting an excellent product from an average one.*

In the case of an alien technology, it might mean the difference between a working copy and something resembling a cargo cult.

'* to detail on this, in the sector where I work many excellent manufacturers are protected from dishonest competitors simply copycatting their original products by the lack of knowledge on how the software has to work.

It could be one of many things:

• A combination of sufficiently advanced precision and size. While we have the capability to manipulate individual atoms, arranging a football field worth of atoms is vastly beyond our capabilities. Or make it 3D and try to build a device with the volume of a family house with a precision of a single atom. Just letting the air come in contact with the half-finished product would ruin it, not to mention any interference from the building process (outgassing or fumes from the atom-manipulators themselves for example).


• The design could be extremely sensitive to any kind of radiation, including gamma rays and X-rays. Maybe the aliens have no problems with it due to some local spatial anomaly or having a home planet devoid of any radioactives and with a crust made of lead, so they can assemble and operate the device underground. But we lack the capacity to create an absolutely radioactivity-free environment due to being bombarded with it from space and from below as well. Even our bodies are radioactive.


• As an alternative to the above, make the design complicated enough and sensitive to even trace amounts of electromagnetic radiation of a very wide frequency spectrum. Good luck building anything complex and precise without using any electronics, letting light touch it or getting human brains and nerves nearby.


• Anything sufficiently complicated and time critical. For example the aliens might have devised a way to stabilize and thus preserve the (for the design) essential extremely unstable isotopes that would normally decay in milliseconds, but the process requires an obscene amount of this isotope. We might be able to synthetise this isotope, but at most a couple hundred atoms at a time, with at least hours between two attempts. Oh, and the synthesis can only happen in a particle accelerator deep under Switzerland, while the assembly process needs a zero-G environment.


• 
  Resource scarcity: the schematics might require a greater amount of some extremely rare but stable element than is estimated to exist on Earth. Like Radon, Tantalum, or something else. (I don't have the numbers at hand, so my estimates might be off the error chart, sorry). Even if this element occurs in a quantity large enough to construct the device, it could be a consumable for it and thus it could be simply not viable to operate the device for any useful purpose without strip-mining half of a continent or distilling the Pacific Ocean for the required "fuel".


• 
  Suggested by @bukwyrm as comment Purity: If the blueprint calls for materials at or near 100% purity (i.e. absolutely no foreign contaminants, maybe not even a single atom) then this criterion could also render the manufacturing process impossible with today's technologies.


• This might be not what you are looking for, as it is less technology than politics, but distrust could stop anything we normally would be capable of doing. If a large enough fraction of humanity would become convinced that the construction of this device would be risky, hazardous or simply require greater than acceptable sacrifices from their part, they could stop the project if the required funds and logistics make it vulnerable. Think of protesters chaining themselves in the paths of trucks, blocking the entrances of engineers working on the project, harassing support personnel until they quit, assassinating leading scientists, campaigning to politicians to stop funding the project, sabotaging necessary equipment or facilities, etc.

There are currently cases of archaeological findings (which were created by humans on earth hundreds or thousands of years ago) that we currently cannot reproduce (some of those are not very credible, others are). We can scan the artifacts, screen them with X-rays and put them under the best microscopes, but the knowledge how these artifacts were created is still lost.

We can put a large number of iron and carbon (and some additional) atoms into a pretty regular atomic matrix that makes the end product (steel) robust but flexible at the same time. But this process requires not only the right ingredients, but also repeated heating and controlled cooling of the material. If the aliens send only the list of ingredients, the material would still fail in the finished artifact.

Even if the aliens send detailled instructions, we might not be able to follow them. If the instruction says to put pure carbon atoms into a solid, cubic lattice, we know the aliens want us to create an artificial diamond. But what if the instruction says to put pure oxygen atoms into a solid, cubic lattice? We'd have extremely detailled instructions but still wouldn't know how to follow them.

You're making the assumption that we could read the schematics

I'm an electrical engineer in microelectronic design. When I compare the schematics that I create to those of a 1973 pinball machine my father owns one thing becomes incredibly obvious:

Someone only versed in the 1973 schematics would have no idea at all what they were looking at when viewing my designs.

First problem: The odds that another intelligent species used exactly the same symbols for the devices as we do are inconceivable. But, as any cryptologist will tell you, if all we have is a substitution code, it's resolvable.

Second problem: The odds that another intelligent species would build technology exactly the way we do is almost inconceivable. He humans tend to think (a) that what we understand of science today is all there is to understand and (b) that there is no other way to do it. What arrogance.

Third problem: The odds that another intelligent species hasn't come up with devices we havn't invented yet are fantastically good. In which case, we have a symbol on the proverbial page that means nothing at all to us.

Fourth problem: Fundamental schematics are massive. They don't fit on paper anymore. So you're assuming we have the ability to "open the computer file," which is dependent on both (a) the software used to view the file and (b) the hardware needed to run the software. Now we have a chicken-and-egg problem: if we need the schematic to reverse engineer the tech, where'd we get the tech in the first place? You need more than the schematic. But once you have it, why do you need the schematic?

Fifth problem: What kind of schematic are you looking at? Today, we use schematics representing many levels of abstraction. A logic diagram (NAND gates...) will tell you how advanced tech operates, but won't tell you how to build "the chip." A functional diagram will give you an even more abstracted view (CPU and memory blocks...). If you have the wrong kind of schematic, you'll stare at it forever and never figure out how to build a thing (well... it might give you ideas about how to build something using Earth tech...).

Sixth problem: Modern schematics tell you what is connected, but not how to build it. Not at all. It doesn't tell you how to dope the substrate, or how close to the substrate the gate must be, or how much encroachment you can withstand during manufacture... You don't actually know anything at all about, for example, a transistor other than it's reference name. An entire file exists (not part of the schematic) that describes the characteristics of the transistor — and even that won't tell you how to build it (well, someone educated in the art could do it, but the point is we're not educated in their art, right?). Even if you had a layout view of the transistor (indicating what regions in 3D space are affected/assembled how), you don't have enough information to build the transistor. There's a fabulous amount of mathematics behind a transistor that a simple symbol on a piece of paper simply assumes is well known — and we wouldn't know it at all. Heaven help us if their math is different than ours or has techniques we haven't discovered yet.

Seventh problem: My thanks to WillK for helping me see this. We'd be unbelievably lucky just to understand the units they use for electrical potential, charge, current, resistance, and every other unit. While we've created highly accurate means of defining these units, they're basically arbitrary — it's the relationship between the units that's mathematical. But remember, our definition of a second is arbitrary and expecting aliens to use the same definition is wishful thinking. If enough information was available on the schematic, we probably figure this one out — maybe. But it'd be a whomping headache until we did. (Think about this, "universal constants" are universal in context, but not in units. The only constants that would translate are the unitless ones: like 𝛑. Unless they use something weird like base-13 math!)

And that's just considering whether or not you can understand the schematic

Most of these are temporary impediments, not permanent

We may not have the means to produce specific compounds required in the schematics. Sure, we have the raw materials, but maybe we don't have the knowledge to combine them in the right chemical process to get the substance they need. Or perhaps we don't know how to refine the raw materials to the proper purity first. Or maybe the schematics require very specific isotopes that are difficult to get in sufficient quantities.

We may not have the ability to operate at the right scale. Sure, we can build complex electronics, but maybe their schematic details microchips at a 3 nm scale, while we're still operating at 14 nm. (or some other subcomponent.) We just don't know how to shrink our designs down enough to do what they require.

Or perhaps they call for some object that is so specific and fragile that it must be built outside of a planetary gravity well, and so we lack the infrastructure to get the raw materials and manufacturing components from Earth to a distance that's a safe distance away, with all of the shielding and other concerns that go with it.

Maybe the raw materials or finished sub-components are highly toxic to humans (but, theoretically, not to the aliens, or they have better protective gear). Maybe it requires highly reactive or highly unstable materials that are extremely dangerous to work with. Perhaps we just don't have the technology to safely build the device.

Politics may get in the way. Perhaps a key raw material can only be found in some nation that refuses to sell to this project. Or they ask for some price that's so far off the scale that the project cannot move forward (whether that's a price in currency or a price in concessions -- would we allow a despotic, genocidal, regime to dictate that they get to select half the ship's staff, for example?) Note, too, that this has a potentially high risk of introducing saboteurs into the equation, which will increase the risks, costs, and etc.

Religion may also place barriers, especially if we are talking about one or more of the Western religions and if those religions come to the consensus that the FTL drive is a threat to their believers, to their power base, or to their faith in general. Note, too, that this has a potentially high risk of introducing saboteurs into the equation, which will increase the risks, costs, and etc.

Industrial espionage or sabotage could impact the project's ability to proceed. If, for example, manufacturer X gets the bid for some component in the process (and thereby gets to patent all the related technologies that go into making it...), perhaps manufacturer Y's less-than-moral CEO decides it is better that no one have FTL than for X to beat them to market with those awesome patents...

Public opinion may prevent the project. The geopolitical mix today is struggling with human immigration, so it is entirely possible that the same part of humanity that hates "the other" in us will hate "the alien other" even more. It wouldn't be impossible for this kind of xenophobia to spiral out of control and crush this project.

Military intervention may also play a role, though this may just be a subcategory of Politics above. But if some segment of the design is obviously a threat to safety, one military or another may decide it best that no one have access to that technology. I mean, if Germany or even USSR had known the US was about to drop an atomic bomb on Japan and had details on that, don't you think they would've tried to disrupt the Manhattan Project?

Can we understand the schematics? That's not as simple as it sounds. Aliens see and think in alien ways. This matters, since even humans don't all read schematics the same way.

"The drawings were in Swedish, using metric units, and read from the
first angle of projection (American practice used the third angle);
the blueprints read “backwards” from American practice, and was much
less precise than needed (the European practice of the time was to fix
small discrepancies by hand)." (Bofor Guns of WWII)

It is therefore possible that we will have to translate the schematics into a format that makes sense to us backwoods humans. How much time and material will be wasted as we try, fail, and try again to make something before we figure out how the schematics work and the units of measure in those schematics? Sure, the aliens can send us cheat sheets to shorten this process, but they may still fall back on assumptions that are intrinsic to them that we have to fumble our way through.

So any or all of the above can present barriers to the project. Can they be surmounted? Sure. But it will take time and effort. So the delays (and the project costs...) will mount up, making the entire thing difficult at best.

The biggest impediment would be precision, specifically if it involves arranging atoms.

Watch this video on Youtube done by the first team to move individual atoms (2011) and you'll notice that although we're able to do it, we haven't been able to do it with every element - and it's far from mass manufacturing scale.

So if the technology required specific molecules to be synthesized, and it couldn't be done through a chemical process (i.e required single-atom manipulation assembly of the molecule) we would not be able to make enough of anything in a reasonable amount of time.

A second consideration is time. Many manufacturing processes today rely on non-instantaneous chemical processes (think of the whole alcohol industry, for example). Many processes can be accelerated and most industries do their best to accelerate them as much as possible but they remain non-instantaneous and can take a long time.

If the technology required a chemical process that took more than a human lifetime to complete, you could argue it would be unfeasible for humans to build it (and impossible for any individual). I don't know of such a process but this is a hypothetical question about technology and science we don't know about yet, so I'll mention the possibility.

If the Alien tech bases on theories that we cannot understand, it might be impossible to build.
Or if we do not have the tools to make the tools to make the tools to make what the sent us.. after all, you wrote that they sent us the plans how to build an artefact, but not how to build the tools to build the artefact.

Politics: We cannot assemble the financial will to construct the alien tech, or we fear the consequences of the alien tech

(I do think there are interesting answers re: the pyramid of technology required to manufacture at high tolerances, or the difficulty of following instructions that we lack the science to understand. However, to avoid repeating content that others have already mostly addressed, I'm only considering the political angle...)

1: Lack of will

The lack of political will for big projects is not a new feature to the human race, and depending on the alien schematics, we might be looking at a national-scale or supernational-scale effort to build the thing. That could be a problem.

Is Europe willing to let its healthcare system suffer to build an alien macguffin? Is the USA willing to slash the military? Is China willing to risk economic collapse by redirecting govt. funds from selected industries? etc...

2: Fear

There could be active resistance to building the alien machine by framing it as dangerous... Be it the existential risk of "are we losing our culture if we develop through aid", the religious risk of "Are the aliens enemies of [religion's] sacrosanct tenets?", or the practical risks of "Are we facilitating our doom if we build the warp-gate / the nanomachine factory / unknown magic macguffin?".

It may be impossible to complete such a project if nations or activist groups are opposed to the point where they would use violence against the project.

Let's say we can manufacture this machine.

You say we have the necessary materials and budget, however here are some issues that could result from it:

1. 
   

   What if the scale of the schematics, while normal for the aliens, is incorrectly sized for humans? The device itself is so small it is unusable for humans, while it would function for the aliens due to their differing size.

   
   
   

   We could attempt to scale up the device itself, however the the scaling causes the device to work incorrectly, and using them en masse leads to errors. Leaving us with having squandered our time and resources.

   
   


2. 
   

   Another possibility is that the device simply won't work for us due to our differing biology. Perhaps we can't dampen the forces it produces to allow to survive at those speeds, while the sturdiness (or fluidity) of their alien physiology allows them to dampen it enough to survive.

   
   
   

   Maybe it produces a form of radiation that the aliens are immune to (or are able to sufficiently shield), while it cooks our bodies even through protective layers and shielding.

   
   



3. The materials on Earth are sufficiently rare so as to only be able to build one of these devices. This leads to a huge fight over which country is allowed to control the device, and maybe it being unable to be built due to irreconcilable differences between them. Even if built and a country has control of it, the fact that we can only have one means that it is of limited usefulness even when constructed.



4. 
   

   We simply don't believe or trust these aliens. Humanity tends to be skeptical be nature, while we may receive these instructions we simply have no idea on how it works or what it will do aside from their explanation. Why would they simply help us for no benefit of their own?

   
   
   

   Who's to say it's not really something that will open a portal for their armies from across the galaxy to invade or will generate a black hole. In this case, the countries would work together in the open to make sure it is not built until they fully understand the implications and effects of doing so, presumably while secretly conducting experiments with components of it on their own, so as to get ahead of possible competitors.

   
   
   

   On the upside, having the schematics will help us fuel our scientific discoveries towards the understanding of the machine allowing technology to improve much faster than it's usual rate.

   
   

Is 2019 technology (not science) sufficiently advanced that given
sufficient raw materials, we could make any conceivable human-scale
artefact that the aliens specified?

No.

It can be too expensive, it can be too dangerous, it can require materials we don't have, technologies we don't have, or we may simply not want to do it because of side effects. "Not want to do it" can range from anything to "it's obviously a bad idea" to "it's unthinkably opposed to our values".

What do we know that we don’t have/know?

1) Power. In Back to the Future they the working gadget, all they needed to do was turn it on… which required 1.21 gigawatts.

2) FTL requires metals or other resources that we don’t have the ability to make in large enough quantities. Anti-matter. Black holes (google “Black hole drive”). Elements with very high atomic numbers.

3) How to deal with Side effects. We can already make flying cars, it’s a bad idea.

3a) FTL gives an individual the ability to crack the planet if misused.

3b) FTL generates so much radiation that it can’t be generated, experimented with, or developed on the Moon, much less the Earth. The aliens just assumed we’d realize this and set it up far away, like Mars or a moon of Jupiter.

Some possible reasons:

• Can't make/obtain materials


• Violates treaties


• People really don't like the idea of building it


• Can't do it to tolerance specs


• Requires too much exotic environments (pressure, temperature, etc)


• Produces lethal pollution, radiation, or similar hazard that cannot be shielded against


• Requires too much power


• Using schematics requires too much computational resources


• Humans too dumb to understand schematics

What manufacturing capabilities do we know that we don't have?

Technologies That We Know We Don't Have (or are developing)

• Genetic Engineering : our capabilities are still limited to a handful of traits at a time, with a lot of testing in-between. Genetic Engineering projects on the scale of planes, rockets, or dams are still outside of what we can do.


• Nanotechnology : we can produce some materials at industrial scales, but our maturity with material engineering at this scale is still fairly young.


• Nuclear : at industrial scales, we can only fission uranium and a few other products. We can not produce fusion of low-energy deuterium, and fusing neutron-free hydrogen, helium, oxygen, carbon, nitrogen and heavier elements up to the iron break-even limit is way beyond our abilities at the moment.


• Transmutation : we are aware that in laboratories and with high-energies it is possible to split or fuse atoms to create almost anything, but this future technology is in it's infancy.


• Manned Spaceflight : we had the ability to send people to the moon, then we shifted attention somewhere else for sixty years, and now we are attempting to re-develop the technology again. However, if an alien message included "capture and bring to your world this ore-body (or prototype) we're sending to you" it would currently be outside of our power to do.


• Deep Ocean Operations : while James Cameron can send a single sub down to Challenger Deep, and while we can drill wells from several kilometers up, our ability to operate in the deepest ocean is very limited. If the message includes "pick up further instructions, we splashed them down in your deepest ocean for the safety of your people" our capability to perform a large recovery is very weak.


• Geography : even in the satellite age, there is a tremendous amount of our planet that is still undiscovered. If the message included retrieving mineral deposits the aliens knew existed in a specific part of Brazil, the Sahara, the Antarctic, or many other places, we would be out of luck.


• Quantum Computing, Communication : while we can create entangled photons, transport them long distances, and reliably read the entangled probabilities, we still have not demonstrated the ability to send non-random useful information along this channel. We have not even proved unambiguously that it is possible. So, we would be in trouble if the alien schematics assumed we'd have sufficient computing power to solve any "localization calibration" that required a lot of heavy lifting computationally.


• Inter-species Communication : we live on a world with a stupefying number of alien (non-human) species. However, we're not even entirely sure that any of them (except us) are sentient. Communication has been weak. In many cases, we're not even sure of their capabilities. If a message assumed we could leverage bats for ultra-sonic quality control of parts, or something similar, we'd have to invent a workaround.


• Gravity : we have only just this year proven that gravity has waves. We are not even close to understanding how to apply this to communication, computing, or other infrastructure.


• Mass : we also only very recently proved that the Higgs field is a real thing and that something previously thought immutable (mass) can actually be changed. Maybe the first implementation is James Woodward's Mach Effect reactionless drive, but we are still very new at that.

It's not a schematic.

Theory of Everything

If we don't understand the science that explains how the thing works, it's because they forgot to include the mathematical formula for the Theory of Everything which is what would make FTL travel possible. Which isn't, because we still can't figure out if there's a cat in the box or not.

All those things you specifically mention are neat things for which we completely understand the physics behind, that we have undeniable ways of representing with Mathematics: the Language of the Universe. It's turtles all the way down, but the universe's Latin is math. To send it in English would be quite arrogant.

Commence Operation Handwave (or the Manhattan Project)

We get to handwave almost all of reality here:

Time.

Money.

Materials.

Manpower.

'Completely deciphered'.

All you need now is a leader. Someone to take that money and employ whatever the world's population can spare from, e.g., food production and health services, to begin taking the materials, for whatever time it takes, to finish the project. Gimme a thumbs-up from a theoretical physicist and we're good to go.

A leader. Someone like Dwight D. Eisenhower, the Supreme Commander of Allied Forces. A logistical genius who decided things like, to win the war, we'd need almost half a million trucks; non-combat vehicles. And to erect the largest edifice every yet constructed, for learning how to build and make the materials for, a device that can be described on the back of a napkin (if you understand the physics), capable of destroying entire cities.

Extinction

That is the only thing that can truly and ultimately stop our progress. Until we exist, we can advance. We did so for as long as we have existed, and there is no reason why we should stop. Eventually, we will reach whatever technology exists anywhere else in this Universe.

Now, provided that the chance of Earth being hit by a random zig-zagging rock of adequate size is non-zero over the time-scale of the Universe, or that the Universe may collapse draggin us with it, or that we may trigger our own destruction (as we sometimes try to), the answer to the other question "Ok, but will we always be able to...?" is

No.

The answer to your question as written is ‘we don’t know what we don’t know’ (addressed by others), but here’s something which may have a big, big impact on the creation and usage of alien technology:

Politics

Imagine for a second if I went to the US government and said ‘Here are some plans for a fusion reactor. The science is beyond you, but I promise if you just follow the instructions, build it and turn it on it won’t blow up or anything. By the way, it was designed in Russia’

The response would be hilarious, and the reactor would never get built. And the Russians are the same species as us.

If your public or politicians have even the slightest xenophobic (or protectionist) tendencies then you can expect that these designs won’t ever be built, not because of any technical limitation, but because there would be unimaginable outcry if anyone tried. Not only that, but decades of ‘the aliens were using us all along’ storylines would naturally predispose us to not trust the aliens.

Then there’s the whole notion of international politics to wade into. Who gets to build the thing? If anyone objects to the thing being built by anyone but them will they drop nukes on it to stop it being built? Who will stop the crazy cults that can undo years of careful calibration and testing with a well placed suicide bomber? Will anyone refuse to sign the budget appropriation bill if the thing is/isn’t included in it? Could the thing be cancelled as ‘the previous administration’s folly’ and leave a two kilometre long tunnel under Texas?

Building this could get so bogged down in negotiations and political wrangling that the aliens give up and go talk to a less neurotic race, regardless of technological constraints.

Now I’m going to go think about something slightly less depressing.

Schematics often contain summarized references to parts which were assembled by a third party. For example, the schmatic on my desk right now references an Allen Bradley PLC, and it does not include any information about what that PLC is, or how to reproduce one.

Also, schematics will generally give precise information about sizes of items, but it's impossible for people to produce items perfectly sized to those dimensions (they might be up to a mm off here or there). For that reason, people who follow the schematics often require an experiential understanding of the tolerances associated with each part. Sometimes a difference of micrometers can mean the success or failure of a project, and those tolerances are not always noted on the main schematic, but are sometimes mentioned in the purchase order for the parts, or they are just understood by people in the industry.

This rule applies to physical sizes, densities, roughness, ratios of fluids, temperatures, material conductivity, electrical resistance, and really any measurable quantity. The number of variable tolerances associated with any project can make it infeasible to note them all in the drawing, and nearly impossible to reproduce the device without knowing them.

One real-world example of this is China's long-running struggle to make a good jet engine. They've stolen entire engines, and schematics for them, and they reproduced them, but their copies just didn't work. It was because they didn't understand the tolerances, and there are a lot of parts to guess at.

It depends...

Do we have the schematics for the tech or do we have the schematics for all of the steps of technological development that lead up to the development of THAT technology?

If we only have the schematics for the Chappa'ai, but we don't have the schematics for the crystal control panel technology, the Naquadah mining technology, the Naquadah refinement technology, and all the other things that lead to the building of a Chappa'ai, then what good does it do for us to have the schematics to a Chappa'ai? The creation of technology isn't reliant only on knowing what is needed to make it, but on also knowing all the steps necessary to get to that point. Leonardo di'Vinci couldn't make a functional airplane, but he understood the idea behind it and made a schematic for what would later be an inspiration in future endeavors. He saw the modern era long before it was even an idea to most people. The problem is, it's easy to say "We need a specific material made in a specific process put in a specific arrangement," but it is much harder to say "This is how we make that material, perform this process, and get it to fill this arrangement." They say our technology is evolving rapidly, but it really is still just a crawl. It's our perspective that makes us feel like it is faster than it really is. Without all of the relevant schematics explaining how we get from where we are to all the way to where that alien technology is, then we can't hope to build that technology until we have finished remaking the wheel over and over and over again.

The biggest question is how determined are we and the aliens to share and build this thing. If these are do-or-die determination there is nothing stopping us from building it.

Examples:

The machine probably has 1000 or millions of parts, and each one is an opportunity for failure. One guy decides to cut corners because its Friday and s/he wants to go home, boom failure * 10000000 people involved.

Access to a fifth, sixth, or seventh dimensions is required.

Lots of other issues.

However, if the alien(s) are prepared enough even these things won't stop us. Here's how.

1. 
   

   They send us instructions how to build 300 generations of replicator from 3d printer up to the latest and greatest 9th dimension model. So generation 1, builds a gen 2 device and so on and so on to gen 300. Within a couple generations we will build nothing.

   
   
   

   Additional each generation is less our technology and more theirs. Generation 1 has to be 100% human made. Then gen 2 will be 99.666% human made and so forth and so on till all the parts are printed by 100% alien to us technology.

   
   

We will feed in any RAW materials and the device will e=mc^2 matter. That is convert all matter placed in the input bin to energy and then back to new matter. So now all we have to do is pour a constant supply of stuff in the input bin. So we connect our sewer system to it, and boom constant supply of raw materials. And all of our trash into the input bin.

Then its starts spitting out parts, and we just lego them together. Eventually with each generation they will be able to print larger and larger objects.

So now at generation 300 the machine is large enough to 3d print the whole unit FTL engine without any intervention from us. Aside from pouring in the raw materials.

Of course we could make mistakes in producing the initial units, however the aliens have though of that. The machine contains (much more advanced versions) of parity data, and error correction. It detects and corrects errors, say part 129 is off tolerance by 0.001mm, the replicator prints a new piece and us humans know the old piece is bad because the duplicate piece is there. We swap out the piece, and production continues.

Yes, generation 300 can print in 12 dimension or more so we have that covered.

Say we can't access dimension 10+ for some reason.

The aliens guessed that might happen, and they have included blue prints for every conceivable combination of dimension including just our 4.

The aliens could have planned for 10 billion contingencies therefore virtually guaranteeing we can produce whatever it is.

Machine produces harmful radiation during product, aliens thought of that and the device generates star trek or better force fields and contains the radiation or other harm field(s) and potentially converts it back to energy recycling back to a harmless state.

They don't know what is harmful to us. Thought of that, it includes a scanner to scan humans and figures out what is harmful to us, and protects us from it automatically.

Yet if we encounter contingency 10 billion and 1 it might all be for naught.

Yet, the aliens thought of that to. The machine opens a micro-wormhole and downloads updates from alien HQ. Reports on the things it didn't expect, and the aliens upload the necessary fixes contingencies. Note the original transmission is one way, but include a list of 5000+ galactic coordinates. 0 by 0 by 0 by 1, 10 by 1 by 10 by 1, .... The computer opens a micro wormhole to each coordinate and attempts to download updates from there.
-----Real example----
--hd radio meta data

TrafficMapProtocolVersionID="1.3"

TrafficMapID="#####"

StationList="(#####,FM123.7)";"(rrrrr,FM98.7)";"(xxxxx,FM45.6)";"(hhhhhh,FM91.2)"

NumRows="3"

NumColumns="3"

NumTransmittedTiles="9"

CoordinatesRow1="(###.55345,-###.81309)";"(###.19653,-###.45617)";"(###.55345,-###.09925)";"(##.19653,-###.74233)"

CoordinatesRow2="(###.19653,-###.81309)";"(###.83961,-###.45617)";"(###.19653,-###.09925)";"(###.83961,-###.74233)"

CoordinatesRow3="(###.83961,-###.81309)";"(###.48269,-###.45617)";"(###.83961,-###.09925)";"(###.48269,-###.74233)"

BackgroundRGBColor="(194,187,96)"

CopyrightNotice="Copyright © 2014 iHeartMedia, Inc. All rights reserved."

I have replaced the real data with fake and ### the coordinates. My radio has one way communication with my radio station, but I still know exactly where they are located.

Humans might get board or just stop building it.

Yup, the device is now printing androids the work can continue day and night until completion.

Need some extra power...print advanced solar panels that absorb light in all spectrum's, way more efficient and power. Have the android place them if needed.

Many good answers have been posted regarding communication barriers, organizational problems, resource scarcity and current manufacturing capabilities.

Let's suppose we had infinite time, infinite resources, no conflicts, the entire alien "tech tree" and perfect communication. Even in those conditions there may simply be hard limits in mind and body to what humans can achieve.

Some ways in which we have encountered limits to our minds:

• 
  Gödel's incompleteness theorems identifies limits to human reasoning (in math). In short: some things are true but cannot be proven.


• It is up for debate whether math is "real" or merely a product of our collective imagination. A set of axioms cannot prove itself.


• The Chomsky hierarchy ends at regular grammars, but perhaps aliens can conceive even more complex grammars to solve more complex problems.

In regards to the body, the aliens might be too different from us.

• They might be 4+ dimensional beings.


• Supposing the universe branches with every decision made, they might be existences that span multiple branches and can collapse themselves into those they like.


• Their composition might be too different from ours, so that certain procedures that work on them do not work on us. For instance, our genetic engineering is not going to work on life-forms that are not carbon-based.

Many industrial manufacturing processes are inherently risky and produce wastes that need special handling. Even today people still get killed in foundries, or poisoned by fumes and we've been messing around with liquid metals for a few millennia now.

What if the alien manufacturing techniques required something truly nasty, or the waste product makes the insides of old nuclear reactors or chemical plants an ecological haven by comparison?

The second half of "Pushing Ice" by Alistair Reynolds may provide some thought. And of course, that means you'd have to read the first half as well so it makes sense. Which is an excellent way to spend a lazy Sunday. :-)

There is an old saying, "The map is not the territory".

There are technologies we still have not recovered from ancient times such as:

Roman concrete

Damascus steel

Greek Fire

In order to manufacture the technology, we would need in addition to the schematics:

1. Methodology required to manufacture the components


2. The tools to manufacture the components


3. The materials to manufacture the components


4. Any infrastructure to support it

Take how computers have advanced from the 1950s to today. Even if we had had the specs to manufacture an iphone today, we wouldn't have the schematics to create the microchips required, the technology to manufacture the plastics and resins we do now, the precision assembly robotics to assemble the components or to mark the circuits.... et cetera. Then even if by some miracle, they pulled it off, they still wouldn't have the code to run it, the network of cell towers to support it, or any way to know those were needed.

There are actually MANY obstacles, as you can see.