[Serious] Could an omnipotent and omniscient god prove that he was God?

[Objectivist]

The only thing that just is without a cause is the universe or the total of what exists.  It's perfectly right to ask about causes within the universe since that is where causality happens.  That's where things exist and act according to their nature.  That's causality, entities acting and interacting according to their nature and only according to their So an Oak tree has a cause and you have a cause, but existence as a whole does not because there's nothing outside of existence to be a cause.  But once an Oak tree exists, it is necessary.  Once your parents have you, you are necessary.  A spec of dust is necessary because it exists.  

What random chance refers to is our inability to predict something.  A dice coming up on two sixes isn't a random chance, it's causality.  If we could measure all the forces acting on the dice we could predict the outcome.  Causality applies within the universe but not to the universe.  That's eternal and uncaused.  When a human being makes a choice that isn't random chance either but causality.  Causality is the identity of action not a relationship between events.  

The universe is all causes, all actions, all relationships, all nature, all motion, change, attributes, everything, therefore it can't be caused.

The total of what actually exists appears to be quite arbitrary if the total is basically this universe or a limited range of universes. Perhaps for you, this doesn't raise any big questions and therefore you're content with what just is, but for me, it's a question still worth considering.

How?  Arbitrary means unsupported by any evidence either perceptual or conceptual.  Once we are aware of some objects then a total is implicit.  An actual infinite can not exist.  It defies the law of identity.  By what means are you aware of these other existents that exist outside of the total and how can we distinguish these other existents from somehting that is merely imaginary?  It's these other existents that are arbitrary and we have a way of ruling them out.