This is where my religion kicks in. As Extratellarian zo?tropist, we have our own theories and ways of explaining on that which are, unlike most highly defined scientific material and religious literature, very logical to the 'less' capable people.
The universe is, as we know, bigger than we can imagine for quite a while. We all know the fact that everything is dynamic, regardless in what time span we're talking about. Everything transforms constantly, people are born, people die, when buried they are converted into food for the worms and such, which on their turn die as well and convert in other things. Inside this confined space there are countless of different conditions which, due to the fact that everything is dynamic, relocate, gain a different form, become part of other compilations, etc. It's very likely that, due to the size of the universe and the fact that the combination of conditions change infinitely, few or more locations would meet the exact conditions for life to evolve. In fact, every time we find out the universe is bigger than we expected, the chance that there's other life on other planets grows as well. So yes, the big bang was possible and any condition that allows us to live and the fact that we are alive are very much possible as well. We're here, aren't we?