From my understanding, the big bang requires that the proto-universe was in a completely homogenous state that was then pushed out of that equilibrium for some reason. But that reason doesn't require non-zero angular momentum. It only requires that a the proto-universe was homogenous and now the universe isn't. And that is what separates pre and post big bang. I could be wrong, I am not a cosmologist. Would be happy to hear from one though.
What causes a perfectly symmetric ball on top of a perfectly symmetric hill to roll down via one side? (Probably quantum randomness if everything else is perfectly symmetric)