One proof for the physicality of God is
1. If to be physical is to be in cause and effect relationships with the paradigmatically physical universe, and God is in such a relationship, then God is physical.
2. To be physical is to be in cause and effect relationships with the paradigmatically physical universe.
3. God is in such a relationship.
4. Therefore, God is physical.
What are the objections?
Some might object to 2., but the argument for this is historical. ‘Physical’ has changed meanings many times, but in retrospect we can see that whatever comes to be understood to be standing in this sort of relationship comes to be termed ‘physical’. Consider electromagnetism, for example.
Classical Christian theology denies 3. God is perfectly simple, and non-changing. He might change the universe, but the universe doesn’t change Him (prayers, for example, don’t actually affect God according to classical Christian theology).
(This is also why most Christians don’t believe in the classical conception of the Christian God.)
Process theology, on the other hand, accepts 3. So, given the above, process theology posits a ‘physical’ God. This is not to say that therefore we understand how God works, or that He works like other categories of ‘physical’ things we talk about.