Well for one, if the laws of physics are not time invariant (i.e. the laws of physics are not the same at all points in time) then energy can be created or destroyed [1]. So that would be quite a shocker.
It's almost an appeal to common sense. (which, admittedly, is often the best argument we have). IMHO there's often a bit of over-confidence among scientists about the universe being 13 billion years old and what happened during the Big Bang, if it just relies on such a common sense argument.
I know it's unscientific to suggest maybe laws of physics are not time invariant across such scales, because until we have a time machine we can't test this theory, but then flipping the argument (that laws of physics are definitely time invariant) is also technically unscientific -- we're basically assuming this without strong evidence.
This goes back to the old debate on the problem of induction in science, (see David Hume, Karl Popper, etc.) and I think it isn't emphasized enough in modern discussions that, perhaps, there's a small chance that these foundational concepts in physics could be invalid.
To the extent that relates to epistemology that would be more like anti-proof I guess? It does not prove that the laws are time invariant, rather it raises the bar to demonstrate that the laws are not time invariant because that means energy need not be conserved. You can not get one without the other without attacking even deeper fundamentals of modern scientific models. So you must either demonstrate the linked claims, which are pretty foundational themselves, or you must overturn basically everything; both of which demand very robust evidence.
Certainly you can't 1) have a model where energy is constant 2) believe there is nonzero energy in the universe and 3) dismiss any model where energy can change as bogus out of hand because you believe it should be constant, without counter-proposing how it even got here.
We have that, it's the big bang.
The argument being:
You can't propose physics ever changed, that'd mean energy could have been created at some point!
Energy was created at some point, wouldn't it be nice to know when?
Everything created at the Big Bang exactly as it is now, stop asking questions.
The difficulty is we don't know what happened in the first planck second after the big bang, let alone before the big bang (if that's meaningful).
We haven't unified quantum mechanics and relativity. Hence we can't be certain that singularities exist, or that the universe started off in a singularity.