Could everything have just happened? Creationists love to point out the improbability of everything, without acknowledging the possibility. Such as, among the billions of planets in our galaxy, it is possible that at least one could have the ideal properties to produce life.
Does God exist? We have no way of knowing for sure of an 'mechanic' God. The common argument is that there appears to be beautiful 'order' and 'design' to everything. But that says more about our perspective than reality. Long ago ancient people blamed the gods for the weather and rock formations, but now we know that natural processes cause these things. Likewise, many today see the complexity of nature as God's order, but science can explain this complexity (evolution, which is well proven).
So does God exist? Well, depends on our definition of God. Who's to say that God is our general conception of God? Most westerners equate God with the bronze age deity of the Old Testament. Such a God would be a simplistic reduction, in my view.
Carl Jung often talked about God as our consciousness. Somewhere in our evolution we developed this awareness, could this be God? Fundamentalists may believe that this takes away from the idea of God, because it is not some anthropomorphic external daddy in the sky. I think quite the opposite, it gives us a more mature conception of God. A God that evolves. And God does evolve. We can even see this in the Bible, between the Old and New Testaments.