But that's where one of the, imo, impossible questions to answer comes up. What happens if the Universe is self-correcting like in all those Sci-Fi movies?
Like in time travel shows, where if you make a paradox, the universe corrects it in some fashion or another so it doesn't exist. Or at least accounts for it.
If that were somehow true in reality, then as the constants changed, they would adjust things as they were to be seen as if they hadn't changed. Effectively rewriting the evidence of the current universe to reflect how the universe would have been if constants were indeed constant even if that's not really the truth.
I know. That's a convoluted response, but while I don't particularly support that idea myself, it sort of shows what I think is important to consider about the idea that the constants aren't constant. That, logically, if they change, they will inevitably erase the evidence of the fact they changed in some way or another.
We have to use the constants to measure the constants. Which is sort of the equivalent of us using our senses to observe the world even though we all know they can be fooled [Insert Matrix connection here].
Simply put, there are certain ... "variations" of rules the Universe could go by that could very well prevent us from understanding it's past.
What you have to realize is that all the information we have obtained for the universe was obtained since recorded history started. i.e. not very long in the universe's lifetime. While we may be able to look at galaxies in the past since the light must travel and that takes time, that doesn't mean what we see is the same as the light was when it left (i.e. thousands to millions to billions to ?????? of years ago).
If we are to assume that the constants don't change based on space difference (i.e. 1 kilo is 1 kilo no matter where you are in the universe), but they can change (for whatever reason) as time passes, then if the light leaves and shows one thing, then, somehow, what makes light light changes (for example light's nature [photon & wave], or perhaps light's maximum speed, or something similarly basic or intrinsic to what light "is"].
If that were to somehow happen, what the light shows may or may not be different because it would change all light everywhere simultaneously regardless of how much time it's spent flying through space.
Maybe even the big bang isn't as we see it, and that was just a point where these constants changed from a universe we couldn't see or understand to one we can. Or something similar.
Basically, when the rules can change and we don't know why, the possibilities are endless in what could be the "absolute" truth about how the universe got from it's beginning to where it is now. It's not really different from the idea that we all just popped into existence, memories and all, 2 seconds before you read this message. We can't test it because we rely on the rules to test it, and that ends up being circular logic by default. Not that we shouldn't try, but I believe we need something that isn't tied to this universe to really understand it as it really is, but then we wouldn't understand it because we live in this universe.
And so, imo, the question is impossible to answer by the ways of science and how things work. But, we should still try anyway. It's what we do.