I don't know why it's assumed that the universe started out with equal amounts of matter and anti-matter, but assuming that it did, it still seems to have started out with some seed of asymmetry in the manner in which matter is distributed, as we see in the distribution of matter in the cosmos today.
So couldn't the asymmetry in amount of matter and antimatter arise from that?
For example, here's an idea I've had using my very limited understanding of such matters and I'd be happy if someone explained why I'm wrong.
I was wondering what would happen if a matter and an antimatter black holes collided, after reading a bit on the subject it seems that once the black hole is formed the information about what it was formed from is lost so they would be both just black holes and merge if they collided.
Now another aspect of black holes is Hawking Radiation which is supposed to produce radiation at the edge of the event horizon drawing on the mass of the black hole for energy.
So assuming the black hole doesn't retain the information about what formed it, the radiation would constitute photons and equal amounts of matter and antimatter by the random chance of which particle from the pair formed at the event horizon falls in and which escapes.
So then if a star formed from only matter or only antimatter (since a mix of both would fly apart) and collapsed into a black hole, and it was left to radiate Hawking radiation, wouldn't it essentially convert one type of matter into energy and equal amounts of matter and antimatter, violating the symmetry?
And if the universe happened to start out in such a distribution of matter and antimatter that there were slightly more denser regions of antimatter than matter, then a small violation of the symmetry would emerge, the rest of the matter and antimatter annihilate and there would remain a small remainder of matter.