I still think that that’s a misuse of the term ‘identity problem’ - mathematically speaking identity is only an issue when you’re speaking of the identical thing, which doesn’t apply if you’re talking about two different times. For a practical example, your blood is arranged in different positions that it was a moment ago, which means that you do not equal your prior self, which would be an identity problem if identity problems worked the way you imply. But they don’t. You’d best stick with calling this a conservation of mass/energy problem, which is a more accurate descriptor and does apply to the situation. (Like it applies to your bloodstream - though presumably your blood flow conserves mass/energy anyway.)
Anyway, on to the meat of your post. First I’ll note that I think the current concensus is that the universe doesn’t have infinite energy, because it’s not of infinite size, which means there’s not space in it for infinite energy to reside. So we’re talking finite energy, assuming that matters.
The way I see it, there are three potential ways to explain the existence of the universe’s energy level:
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There was an external source that supplied energy during in the creation of the space-time continuum, which then manifested inside the space-time continuum as the energy/matter we’re familiar with.
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The law of conservation of energy does not apply to the creation of space-time continuums.
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The universe has zero energy.
If there are any that I missed, please point them out, but I think this covers all possibilities.
So. The first option is the most intuitive to people, since it meets both the expectations that the universe has positive total energy and that the laws of conservation apply universally. (Or rather, extra-universally.) The problem with it, of course, is that it presumes that you’re not talking ex-nihilo creation after all, and therefore doesn’t explain where everything came from after all. At best, it shunts off the question to that of where the thing that created the universe came from.
The second option seems unintiuitve, but isn’t necessarily, because what we call “energy” in this universe may not be equivalent or even meaningful from an extra-universal perspective. Take for example, if I’m writing a book. (I do like books/movies as an analogy to the space-time continuum!) In that book I can say, “And there were thirty tons of gold there.” Making the the gold appear in the story doesn’t require me to pay for or otherwise acquire thirty tons of gold - because gold in the story isn’t anything outside it. The law of conservation of precious metals doesn’t apply when creating the book - even if I have a strict rule that in the book I have to keep the total amount of precious metals within it perfectly consistent all the time.
Perhaps interestingly, option 2 is also the way Christians explain the existence of their god, though they may not realize it. Presumably God gets energy for free, not needing to obey the laws of conservation, so we’re already working in this realm. A little less obviously, when they assert that God has always existed or whatever, they assert that the energy that goes into him simply exists, without cause or explanation - similarly having popped into existence without regard to the conservation of energy. (This goes double when you realize that an infinite negative timeline is impossible and thus the god can’t actually have existed for infinitely long, meaning that at some point his existence -and energy- simply began, ex-nihilo.)
The third option is of course the one previously pointed out, which I’ve been told is currently being floated as possible explanation by the scientific community. Personally I don’t know many details about it (I’ve said I’m shamefully ignorant, and haven’t even got around to watching the video), but I am able to comment that it’s a pretty elegent-sounding solution for the ex-nihilo question.