Are there any scientists here?
Whatever showed up would be measurable, to some degree, and we could make theories about the nature of this new phenomenon, and test them, and given the assumptions of the question, they would be reproducible. We would set about discovering the capabilities of this god (say it was Thor or Loki or Hera), and then we would behave appropriately, so as to maximize our utility.
It’s not as if this hasn’t happened before. Galileo and Einstein each, essentially, discovered a new “god.” I.e., something that dramatically changed the way we interacted with our universe. This would just be one more force, and we’d have to discover it’s nature. Perhaps it would behave randomly, to some degree, and be unpredictable. Perhaps it would want us to do things we consider strange in order for it not to kill us. Who knows?
Really, it doesn’t matter what nature the god had, and it doesn’t matter what we “believe” about the world. The world will act the way it acts, and if we try to violate laws, we will suffer the consequences. Anyone want to try violating the laws of the god named Gravity? How about Radiation? I thought not.