Early after Big Bang, could small parts of matter and antimatter have drifted away in opposite directions and thus still be able to maintain anti/matter balance, but keep local isolated pockets that are too far from each other to react, so that visible part of our Universe would have been in one of them?
Update: added more detailed description of proposed mechanism: Because of the very fast expansion during that time, some percentage of particle/antiparticle pairs could fly away from each other faster than they could interact with each other or other particles with opposite charge. The mechanism could resemble the one that causes Hawking radiation at event horizons of black holes.