There are several answers depending on how your question is interpreted.
See Hacking Matter by Wil McCarthy, wellstone, and my other answers here where I mention it.
Maybe that's what you mean. A device might seem like it’s made from mundane metals or amazing materials unlike anything we know, but is actually not made from natural atoms, but from wellstone. If sufficiently damaged it can’t operate and exposes itself as normal-matter semiconductors and quantum wells.
If you say it is made of atoms, but are fishy, then I would say “no”. Any exotic atoms or states of atoms are not stable.
Note in the first answer though, a gross test may make it seem to be atoms of some familiar element but it’s not really; the behavior is emulated on a scale larger than single atoms.
Sure, molecules and nano-layers and composites can be engineered, and are different from natural materials and different from engineered materials of a different era.
A 18th century jeweler might not be able to tell that a substance isn’t a precious gem or metal. But I don’t think it would be confused with another material by an expert. A lay observer might think “shiny grey metal used to make dinnerware, not pewter or bronze but neutral colored” and presume “sterling silver”. An expert will say “the color is off; amazingly non-reactive; melts at wrong temperature…” and will come up with aluminum if it was known to that culture yet.
For gems, earlier cultures might have no way of identifying the composition, and there is enough variation in natural gems that it might be accepted as a rare sample of (something).
Plastic might be more interesting. Wax or shellac or some such, with the details of just how marvelous is is being lost on them.
The Roswell incident may have been poteniated by the bizarre unfamiliar materials involved.
But bring that up to today: a material can be subjected to spectrographic analysis and mass-spectrometry, revealing the exact tally of which atoms are present. Cutting-edge tech like at SLAC can map the exact arrangement of how molecules are put together.
So if materials are truly wondrous, people can discover “ooh, the superconductor is made like this” and read out all the details on an atomic level.
Knowing how it’s made on the atomic level won’t help them in fabricating more of it, though.
What if the material is not a simple substance, but has a huge complexity like living cells? We can grasp the crystalline structure of a mineral, but “leather” is harder to figure out on an atomic scale.
Nanotechnology, if not wellstone, may be more like living material and hard to grasp on a level smaller than single cell units.