SBF...We may not have the full answer to self awareness (consciousness) but whatever it is must be true of 'lower' animals as well.
Invoking statistical possibilities as evidence of providence is a misuse of math. Every single moment in time and space is statistically impossible but the moment it happens is 100% likely. Statical analysis has its place in a localized closed systems (like flipping a coin, heads) but not in predicting every contingency of the universe; (what are the odds the copper formed in a supernova would accrete in the earth's crust, to be mined, to be eventually minted into a coin, to be in your pocket, to be flipped by you and get heads. The odds of predicting that would happen are beyond the scales of mathematic possibility and could mistakenly lead to the conclusion that some supernatural force willed the coin to be heads.
So..., we are left with concluding every single happenstance and contingency is predetermined by supernatural forces, or, that events naturally play out in a sequence beyond our ability to mathematically model. Most folks would not attribute supernatural influence in the countless mundane particulars of every moment but get all philosophical about themselves.