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

[Neo-Scholastic]

I think the real question is what could a god do that in principle could not be faked by, say, advanced aliens?  By prove I presume that you mean make so that we believe it is undeniably true that God exists.  Unfortunately, many things that fall short of a god can do this.  On the individual level, all it takes is a brain tumor or epilepsy.  So the question turns on God being able to provide us with a judgment that is infallible.  Short of changing what we are I do not imagine that this can be done.  The idea that the communication channel that runs from the perceived to the perceiver is wholly dependent upon the properties of the transmitting entity is old and fraught with problems.  As much of our perception is within the purview of our brains' operation, it doesn't seem possible to eliminate potential sources of error.

This of course hinges a bit on what you mean by 'prove'.  If by prove you mean something less than establishing absolute certainty, then I'm not sure the question doesn't lose its value.  We already have people convinced by evidence that provides less than complete certainty of the conclusion.  That's a sliding scale with no well-defined stopping points.

I have to admit that I do not fully understand of the OP question. IMHO wondering about God is just as important as knowing anything specific about God.* Admittedly, I personally find Divine Hiddenness perplexing and occasionally troubling. At the same time, I do not see Divine Hiddenness as a stumbling block to faith. As I see it, the Christian lives in the understanding that creation is fallen, that it is less than it could be. IMHO creation is apparently absurd in the existentialist sense. I truly sympathize with true existential nihilism - the intolerably brief ephemera of meaningless human existence bound fore and aft by silent eternities. I get it. The sentiment lends itself to atheism. But I am not an atheist. Despite the incorrigible reality of the Nietzschean Abyss staring down at me. My wondering heart ponders what Reason** says must be there yet cannot be directly seen. The so-called "Negative Way" is the direction from which I approach where I hope to find God. I look for God in the outlines of what seems to be missing most from the world.

All that said, it doesn't address the notion that God's existence should be obvious. Except...should it be obvious? As obvious as what? Material things? Physicial events? Personally, I do not think about heavenly things in terms of material bodies. And for me, prayer is more about trying to discern and conform myself to God's will than it is about pleading for an intervention...expect perhaps for the Lord to provide spiritual comfort to remote Others. Nor is prayer a substitute for action or defense against consequences, IMHO.

There seems to be a modern demand for certainty. Some people, quite a lot really, need the comfort of answers-that-satisfy dressed up as certainties. And while I do not believe this is limited to to religious people, there are prominent and popular people who abuse the religious sentiment with slick doctrines that cover too much nuance. So I am not unsympathetic to skeptical criticisms of religion in this regard, I just think it is a mistake to think of this as an epistemic temptation limited to religious thinking. Some people just need more certainty about certain things than others. Well,...kinda to be expected really.

* Of course willingness to express uncertainty about articles of faith is not a universal sentiment among the faithful.
**  Whether human reason is capable of discerning Absolutes or instead only creating cognitive artifacts contingent on our biology is IMO a primal epistemic choice that must be made without recourse to evidence.