There are various ideas floating around about how God (were God to exist) could intervene in the world in subtle sort of way. What I want to point out here is that, if two of these ideas are unified, one gets a nice coherent picture of how God might interact with the world. 

The first idea is that the standard neo-Darwininan evolutionary account is right, or pretty much right. The only detail to be filled in (or potential modification) is what the source of the “random” mutations is. The mutations are random in the sense that they aren’t controlled by the evolving creatures, but (according to the first idea) some of the mutations are caused by God. In this way, God had a role in shaping the evolutionary processes that led to our existence.

The second idea is that, due to quantum-mechanical indeterminism, God can intervene in the world in a non-miraculous way. That is, there would be no violation of the laws of nature if (say) God decided that a particular radioactive atom should decay at a particular time — according to the laws of physics, there was some non-zero probability that the atom would decay at the time, and so the event of the decay doesn’t violate the laws. 

Combining these two ideas, one get the picture where God occasionally intervenes at the quantum level, and sometimes these interventions cause mutations in creatures, and that shapes the process of evolution.

It’s interesting to consider we could get evidence for the existence of a God who intervened in the world in this way. Suppose that we were able to look at a random statistically significant sample of the mutations that have happened, and we discovered that more often than not, these mutations benefitted the creatures in question. This could just be happenstance, just as it could be happenstance that one flips a coin a large number of times and gets significantly more heads than tails. But my sense is that finding a preponderance of beneficial mutations would provide some evidence for the existence of God. 

All this (by the way) provides another bit of evidence that (in principle, at least) one can get scientific evidence for the existence of God.