You're thinking of the universe in a very classical sense. Our current understanding of physics is that quantum mechanical outcomes are truly random. Not just that we don't know what will happen but that it is inherently not predetermined before it happens. You can read up on Bell's Theorem (http://en.wikipedia.org/wiki/Bell's_theorem) if you want to learn a bit more about this.
If you "ran" the universe over again from the big bang, then the probability that you would exist is essentially zero. I don't know enough about neuroscience to speculate on whether quantum mechanics has any relevance to brain functions over the course of a lifetime but from a physics standpoint it isn't inconceivable.
On a more philosophical note: if there is some true randomness in how our brain works do you think that that actually gives us any more control over our lives? It doesn't really change anything in my view.