A god doesn't have to be sentient for people to believe in it as there are plenty of pantheists. God = nature. God is in everything, etc.
However, a painter is not a painting and an architect is not a building. In the same way, the creator can not be part of the creation.
This would mean trees, rocks, eagles, etc cannot be a god. I don't think it limits physics from being a god though.
What I think would limit physics from being a god is that its a set of rules that will always behave in a particular way. So physics is not a god because physics is a force, a law, or a rule book. However, a god could be described as whatever entity, separate from the creation, that is in control of physics, chemistry and biology and determines how they function. This entity could, perhaps, change these rules as they see fit.
