What does the evidence show? It doesn't show mutation and selection. As far as I know, the scientific evidence simply shows the killing off of particular kinds of bacteria by antibiotics.
I'm certain that God created the world from nothing, and that mankind has descended from its original parents, Adam and Eve. The rest is speculation, which can be informed by our observation of nature.
Now, which is more likely to happen? God, or mutation?
8-) God is the ultimate cause of everything (excluding the evil chosen by men and the pure spirits). Mutation may be the proximate cause in this case. But that's not my understanding of the evidence.
Further, which one can be proven and which one can't?
Good question. What evidence is their for your position?