Three notes:
- Firstly, quarks don't exist in isolation.
- Secondly, Pauli-E says two fermions can't occupy the same quantum state/have the same quantum numbers. So even if quarks existed in isolation, they wouldn't have any problems because of the Pauli principle since basically they'd have different spatial locations.
- Thirdly, a particle spontaneously changing its four-momentum would violate something like Newton's first law (which holds in special relativity, but I don't know about GR... as I haven't gotten that far in this class!)
Then, I think you need to think a bit more about this before you arrive at its "logical conclusion." If you take ONE single particle, and make it move away from some point P in space time for like, 100 billion years, and then spontaneously jump it back to the beginning of time to have it travel out in another direction, then in essence you've altered the future of the particle, and it has never traveled 100 billion years, and so it will never see "itself" again.
Were it to travel back like fifty years and alter its own course, similar things would occur. It'd be rewriting itself.
Ergo, you'd never see a "big bang."
If there were a parallel universe theory, then one couldn't travel backwards in the same timeline. Only "sideways" to other timelines. Then you just end up with a bunch of parallel universes with particles going in different directions. You'd never see a big bang in this case either.