The convergence at a later time sounds highly improbable. The total state of the universe is so large that this would only work if there was something forcing the timelines to converge and never by chance.
The question of convergence then simply boils down to: Are there any possible states of the universe that can arise from more than one prior state. Based on my limited quantum mechanics knowledge, it seems the only place this might be able to happen is in black holes: https://en.wikipedia.org/wiki/Black_hole_information_paradox
If there were two opposing forces, always exponentially self improving towards maximum efficiency in two opposite sides: 1) ordered/creative/perfectionist/preservative/etc, 2) chaotic/destructive/disruptive/etc... suppose our universe sits roughly in the middle of these two, does that not seem to explain where we are?
Also, given the seemingly limitless propensity of the universe towards balance, and its apparently limitless capacity in both regards, it would seem natural to infer that both forces keep going in ways beyond that which we can directly observe.
Intuitively, certainly, it seems very right. Of course, it also gels very well with countless esoteric/mystical beliefs going back eons as well.