There is obviously a whole lot we don't know here. It had to be a solid projectile, otherwise it wouldn't have gone through the airspace inside the tank, and it likely wasn't DU, so the tungsten idea is good. Shaped charge penetrators are generally made with very soft metals, like copper, so there would be a good deal of copper splattered around, which would be easy to find. Also, a shaped charge, being hot enough to melt the metal, leaves a rather distinct pattern in the remaining metal as it recrystallizes. Not distinct from each other, but distinct from a kinetic penetrator, or a pyrokinetic like DU. DU also would have left particles EVERYWHERE. At the very least, I can guarantee that we know just exactly what it was made of. Everything leaves fragments, and those fragments can be easily identified by a skilled metallurgist. Once we know what the penetrator's makeup was, we can begin to identify it.
The main problem with punching holes in tanks is that you need a great deal of energy to do it. If you've ever seen the actual size of the APFSDS-T penetrator, you'll be amazed that something so small can be pushed so fast. So something had to fire this kinetic penetrator (assuming that we're actually getting the information that I think we are and it isn't a shaped-charge) REALLY fast. That something is likely relatively large. This isn't some hoss AK round.
So, it's either that, or somebody used a really neato laser gun, which, while unlikely, is a really cool thing to think about.