[comicjk]

It is possible that there are other stable particles besides the ones we know now (like protons, neutrons, electrons, photons, neutrinos, etc). And maybe they can form stable arrangements which are not atoms, but which can still interact with ordinary matter. In that case you could have a material that was not made of atoms.

I don't think a lump of such material is in a warehouse in Nevada, but maybe it exists somewhere in the universe.

[krapp]

I would think those would just be made of different kinds of atoms but OK.

[andrewflnr]

An atom is a particular type of arrangement of protons, neutrons, and electrons. If something is not made of protons, neutrons, and electrons in that particular arrangement, it's not made of atoms, by definition.