University Philosophy? I'm not an expert in university philosophy curricula, but I'll speculate as follows: the AOTC would show up somewhere in the curriculum but is unlikely to make an appearance in an Introduction to Philosophy subject. The AOTC has an entry in the Internet Encyclopedia of Philosophy, the Stanford Encyclopedia of Philosophy, and Britannica.
Plato's cave? No.
Has anyone said Existentialism yet? No.
Is Existentialism the AOTC? No. (I'd put that more in the vicinity of Spiritualism on the M-m scale.)
Does it entail a belief in predestination? You just had to ask that, didn't you? No.

Enjoying this? Yes and No. Whenever an AVMA takes this long, I worry that either I have made it too hard or that I have inadvertently misled people with a less than perfect answer.
Old Greek? The idea of the AOTC can in some sense be traced back to the very earliest days of recorded philosophy, which of course includes quite a few old Greeks. That said, I don't think the AOTC is associated with a particular OG who was a "major proponent". (It's not like, say, stoicism, where—if you know about the topic—you'd immediately link it to Epictetus.)
Simulation hypothesis? No.