Re: But we do already know that it annihilates when it comes into contact with matter.
"Which means that the Big Bang explosion must've happened in such a way that matter and anti-matter flew in opposite directions with opposite spins. Because that's the only way they could avoid coming into contact with each other."
It seems to me that the earlier comment about the antimatter flying off in the opposite direction *in time* into another universe with time flowing away from the BB in a different direction than ours sounds like a nice solution. I am not knowledgeable enough to say why this may not be true.