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

[Objectivist]

your existence is necessary because your existence is a fact.  To understand this you have to recognize a distinction between what is called the metaphysically given and the manmade.  The metaphysically given is all that comes about without human choice as an input.  The metaphysically given could not be different and it could not have failed to occur.  The metaphysically given can not be judged true or false, it just is and could not be different.  It's the result of entities acting and interacting with each other according to their nature.  All actions are actions of entities, there are no floating actions and the nature of the action an entity takes is determined by that thing's identity.  Contradictions can't exist because that would mean some entity acting outside of or contrary to its nature.  If entities could act contrary to their nature, we'd have chaos and no knowledge would be possible.  

When it comes to human actions, they could have been different.  By our nature which is metaphysically given, we have a volitional form of consciousness.  We can depart from reality within the contents of our minds either by making a mistake in thinking or by deliberate evasion.  That's why all products of the mind must be judged true or false,
right or wrong, and the metaphysically given is the standard by which we must judge because it's impossible for the metaphysically given to be 'wrong'.  Once again we see the axiom of existence/ identity acting as the base of knowledge.  

So it's true that you didn't have to exist, your parents could have chosen not to have children, but once they did choose and you were born your existence is no longer potential but a full fact.  If you didn't exist we'd have a contradiction that can not exist.  Facts are absolutes once they are facts.  That's what I mean about your existence is necessary.  That's why it's so silly to talk about the odds of life developing.  Life as such is metaphysically given, it could not have failed to happen so the odds were 100% that life would happen on Earth.  There is no such thing as random chance, there is only our ability or lack to predict things.

Ok, so since reality (at least outside of human actions) is "metaphysically given", and there is no such thing as random chance, then is it conceivable to have reality be the way it is now (instead of another way) without random chance playing a role here? If something "just is" with no reason behind it, doesn't this suggest some form of indeterminism?

Fair point about what you said regarding cognition and knowledge in the next paragraph. Can't say I disagree there (well, aside from a couple of sentences).

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.