Mostly because space and time are most likely a result of the Big Bang. For all we can tell, "the beginning" was an infinitely dense singularity of space time - there is no "very far from the Big Bang", because, there's no space.
Yes, you can somewhat debate that - we're not entirely clear what happened in the first 10^-33 seconds - but we don't know anything about that.
So you might as well say "what evidence is there that the universe wasn't the spawn of two extremely short-lived green bunnies", and the answer is "none", too.
I thought that theory had issues with quantum gravity?
But either way, inflation would happen in that 10^-33 span I mentioned above. We simply don't know.
And even if we assume it holds, inflation is an extremely rapid expansion of space-time, so the idea that there were things "very far from each other" still does not really hold.
And IIRC, Penrose and Hawkings disproved the idea that inflationary models can avoid an initial singularity[1]. I'd be somewhat surprised to see them disproven.
Yes, you can somewhat debate that - we're not entirely clear what happened in the first 10^-33 seconds - but we don't know anything about that.
So you might as well say "what evidence is there that the universe wasn't the spawn of two extremely short-lived green bunnies", and the answer is "none", too.