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Congrats!!! By successfully navigating this insane maze you've now 'proven' that you can obtain funds. You'll be made to jump through a series of hoops, but assuming your publication history is at all reasonable, you're pretty much ready for going straight from grad student to PI. I highly highly suggest skipping postdoc hell if you have any chance at all, but if you can't, just repeat whatever magic you just did and spare yourself the pain of staying there too long. Having your salary go from 36k to ~100k (without passing through the 50k mark) will feel very good.
Good luck with the meiosis project! Rooting for ya!
I have a very limited understanding of this subject, but this is my best attempt at constructing a coherent answer: it's an open scientific/philosophical question.
Anything in scare-quotes ("Like this") below is a word or concept that I only have rudimentary, incomplete, or mistaken understanding of- you have been forewarned.
Currently, our best understanding of the time evolution of the universe is given by the standard model of particle physics, which is quantum mechanical and uses the Schrodinger wave equation to predict the behavior of subatomic particles like electrons. The Schrodinger wave equation gives PROBABILISTIC answers, and you only get "waveform collapse" and "the application of the Born rule" when you actually interact with the system ("make an observation" or "cause decoherence").
Now, there are some interpretations of this framework that basically say: that's it. The bedrock of reality involves random wavefunction collapse and you interpret that by handwaving or postulating Everett/Many-Worlds branches or whatever woo-woo you want. There are other interpretations of the framework that want to salvage pure determinism by insisting on unobservable "hidden variables" that secretly determine how a waveform will collapse, but a guy called John Bell created a thought experiment to test that and eventually someone actually ran the experiment for realsies and basically if there are hidden variables, they can't be "local" which I roughly understand as a fancy physics word that means 'dependent on spacetime coordinates'. Hidden variable theories totally work in non-local interpretations of QM (e.g. see "Bohmian pilot wave model"), but many physicist don't like those because it causes (even more) problems with General Relativity.
TL;DR / to sum up:
If there are no hidden variables in QM/QFT, then randomness is an intrinsic and foundational aspect of reality, so after "rewinding" the universe, differences will eventually accumulate due to differences in the way that the waveform of subatomic particles collapse.