It's a game of odds, really, when it boils down to it.
You have so many chemical arrangements that can occur naturally, some of them are self replicating. Given enough time (or if you prefer, enough chances) anything even remotely possible, however improbable, will occur with certainty.
The "prime replicator" would be by no means worthy of survival in today's time. In fact, it would likely be so incredibly mundane, it likely wouldn't even get noticed if it were sitting right under our noses... it's far too simplistic.
What I'm trying to get at is the mind bogglingly simple nature of the prime replicator. It barely even classifies as a life form... most would argue it isn't life yet.
Eventually (and I'm talking hundreds of thousands to billions of copies) with enough copy "mistakes" (and most of those mistakes ceasing to exist because of obvious failure to replicate themselves or exist in the environment) a very tiny fraction of the mutations begin showing more complexity.
... and more.
... and more...
I believe we've located two other prime replicating branches of life thus far here on this tiny planet... though, they didn't amount to much. But, we know that the "genesis" point is certainly not a unique event. It occurs naturally... and as far as we can tell, usually doesn't make it very far in its incredibly simple and fragile state.
It's good to be sceptical... though... reality tends to assert itself, regardless of how puzzled we are by it.