Why would we do it? We wouldn’t, really, but I think the thread is meant as a hypothetical to see if it’s possible.
That depends on what you mean by perfect. Natural materials like stone sometimes just can’t be found, even if the quarry the stone came from is still producing stone, frequently the stone is slightly different from a different area of the quarry. Also weathering is exceedingly hard to duplicate, but if you say “enough time and money”, it can done.
Possibly not what you had in mind- not a structure, but an engineering feat was the Paris Gun of WW1. It was never captured, the plans were destroyed and as far as I know it was never replicated.
But today we have ICBMs. To quote me from above, these are a million times better. So of course we could replicate a Paris Gun if the fate of the world depended on it. It would be much easier to do than to replicate a Saturn 5. And we’ll do that when the need arises. Except for the cost and bother, which we’re ignoring, these are trivial problems to modern technology.
Rebuilding a working Saturn V is actually something that fits the OP, within a specific constraint. We will build a sufficiently large rocket and launch payloads to the Moon and beyond. It will probably not work exactly like a Saturn V, and have component parts built like the Saturn V’s.
It would accomplish the same task, be similar sized, and could even be built with similar technology (liquid fuel, staged booster chemical rocket). And yet not be identical, even if the outward dimensions were copied.
Do we need to build circuit chips identical to the Saturn V’s? It isn’t required to make a working rocket, but if we want to replicate the Saturn V, that may prove challenging.
I, personally, feel like that could fall in the realm of the “artistic” variances I’m allowing in things like the black Taj Mahal.