As we cannot observe anything before the Big Bang, then any such concept naturally falls in the realm not of physics, but of philosophy. Which means it’s even more mutable than physics.

From where we are, unable to directly observe even the Big Bang itself, “before” and “outside” are essentially meaningless.

As for why not immediately again? There’s a few possibilities here. There is, of course, the anthropomorphic principle, which would say that in any case where it did, we would not be here to observe it or, at the very least, we’re in the last of such a cycle.

Or, of course, given time only exists within the created universe, “immediately again” could be after our entire cycle of existence.

I’m not up enough on math to quite follow the rest of your model, unfortunately, but “so small that its existence is denied immediately” leads my brain to consider quantum decay, which may itself be an essential property of time.

(No, I will not apologize to anyone reading this).