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Evidence
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Well, again you're using terms of time to describe the birth of time, so no that's not what I think because that statement doesn't make sense. But I'm being pedantic, I'm sure you meant "what if our's wasn't the only big bang?" And to that I can confidently say "maybe?". It's an interesting question but it's just not a scientific question. According to big bang theory, our universe, space-time and all the matter and energy in it, began with the big bang and we still exist inside it. Other big bangs, if they exist in some higher medium, are simply outside our scope. We just can't design tests to answer those questions. Best we can tell scientifically is where our universe started.
Again maybe? You're kinda putting words in my mouth. Idk if our universe is the only one, it's impossible to know. My original point was that time as defined by general relativity could not exist before the big bang because it was itself a product of the big bang.
What I meant by "what if it wasn't the first big bang?", was that what if it wasn't the first of our own universe? I mean what if space will at some point stop expanding and start contracting. Pull everything back close together again. Then theres another expansion just like what we're currently in now. The best scientists, physicists, and mathematicians haven't been able to work out a lot of major thing about our universe or how it works or even if it's flat or folded in on itself yet. The data and tests/measurements don't exist yet. So until that can get worked out into a theory, it's silly to say time began at the expansion.
Last I heard scientists were leaning more toward the ever-accelerating expansion "heat death" theory then the expansion-to-contraction "big crunch" theory, but it's not set in stone yet. But even if "big crunch" came out on top, assuming that the life of the universe is cyclical is pure conjecture. It could be right, but it's unprovable, so we'll never know.
As for the existence of space-time before the big bang, I don't know what to tell you, I'm just quoting theory. By definition, the big bang is when space-time came to be. If the big bang was the result of an ancestor universe's big crunch, we can't assume that the same space-time carried over, let alone that the ancestor universe even had something analogous to space-time. Barring some insanely massive breakthrough, it's simply unknowable.