I don't think mind designs are dependent on their underlying physics. The physics is a substrate, and as long as it provides general computation, intelligence would be achievable in a configuration of that physics. The specifics of those designs may depend on how those worlds function, like how jellyfish-like minds may be different from bird-like minds, but not the common elements of induction, analysis of inputs, and selection of outputs. That would mean the simplest a priori mind would have to be computed by the simplest provision of general computation, however. An infinitely divine Turing Machine, if you will.

That doesn't mean a mind is more basic than physics, though. That's an entirely separate issue. I haven't ever seen a coherent model of God in the first place, so I couldn't begin to judge the complexity of its unproposed existence. If God is a mind, then what substrate does it rest on?