Why not posit that (in any given big bang) there will be some excess of one or the other polarity of matter, as a result of Quantum Uncertainty?
Not that difficult to envision.
During the early yocto seconds of the Big Bang, in the "primordial soup" stage when particles were very close together, particles and anti-particles would bang into each other at random, instead of each hitting its exact counter part.
For instance, a muon banging a positron would release energy plus quarks, since the muon has greater mass.
Enough mismatches like that would result in an random imbalance of matter and anti-matter, and further annihilations would see one or the other become dominate.
At least that's how I view it.