Bullshit assumptions. Why don't you instead prove the universe is *not* finite
The universe is finite. Indeed, within the observable universe we have a rough idea as to how many particles there are - 10,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000. 10^80.
But even cosmologists who have spent their entire careers trying to refute universes that end in various iterations of Boltzmann brains, like Sean Carroll, essentially concede the issue when they argue that the universe sliding other another universe is more likely than Poincare recurrence of a self-identical universe at the end of
this universe. That just repeats the problem once-removed.
and that an identical quantum brain *would* share your stream of perception.
The principle of identity should be inviolate in any universe with properties like ours. A = A. (Also, describing this as a "quantum brain" wouldn't be right; it's created by fluctuations in entropy in space. It just happens to share your quantum space to an arbitrary degree.)
I'm not saying you're going to reincarnate as a butterfly in a dream (or a butterfly dreaming he was you) or anything of the sort. I'm saying the most likely sequence of events is perceptual incarnation as Boltzmann brains and fetuses, with the occasional perceptual rebirth into a probabilistic universe akin to our own within some degree of tolerance. If this latter holds, it's likely that the entire history of the world up to the moment of your birth (or perceptual awareness, which is less definable) would be identical. And if this holds good, it's quite possible that reality would indeed start to diverge from the moment of your birth, each moment being probabilistically distinct from any counterpart the further removed you were from the moment of perceptual awareness. At the next instant your perceptual awareness becomes capable of recognizing itself, bam, you're a self.
Again, no spirits, no souls, just identity and an endless range of likelihoods. I'm not even invoking karma, although it would seem likely that any state of existence arbitrarily like this one is arbitrarily similar to it the closer your perceptual awareness would be to it in the cosmic chronology. I'm not saying that your quantum spirit migrates to a realm where it communes with spirit guides to determine your next steps.
What I am saying is summed up in two words:
time and
probability.