The best thing I could think of in known physics that could provide an interface to some deeper controlling level of reality, if you will, would be the randomness of quantum measurements. They look uncorrelated and truly random in all experiments, but a god-like being could use them to subtly influence the way of the world without violating the physical laws themselves. I think this was the favourite hypothesis of people like ken miller, who is a catholic evolutionary biologist who played an important role fighting ID in Kitzmiller vs. Dover
The fool hath said in his heart, There is a God. They are corrupt, they have done abominable works, there is none that doeth good.
Psalm 14, KJV revised edition
