I think you just need to define "Consciousness" and "Divine", and the answer will pop right out.

There's 40 or so definitions of "consciousness"; and even Christians (let alone all the other religions) don't all agree with each other about what does and doesn't have it and what the implications of this are.

But we can say there's no gap in physics into which unknown forces could manifest actions on our bodies. (This is different from saying "proves the absence", it is only that you'd need to come up with something as powerful at explaining the world as all known physics in order to create room for such a thing).