Imagine a delicate ecosystem of fragile bacteria that is dependent on the pH of the water it lives in. Now imagine that you poke your dirty human finger into that ecosystem. The moment you interact with a system that you exist outside of, you become part of that system.
If the Hand of God truly does intercede in aspects of reality we would be able to track and measure the outside force as it entered the equation of any system we intimately understand. We would be able to trace the moment the system went haywire from an anomaly. It would be documented in every field from medicine, to cosmology, to plate tectonics.
If the dew point mysteriously raises enough to rain on a barren Somali village the science of meteorology would have to account for the change using existing scientific theory or the current theory would be discarded.
In fact all theory would need to account for a “G-factor” when explaining and predicting the behavior of a natural phenomenon. Scientists would have to describe a process that occurs only in the absence of divine intervention. In all fields of study where we could account for the traits in a closed system, there would be a clause for the occurrences when all of the rules break down and something mysterious happens.
The G-factor does not exist in science because we can account for the changes by natural phenomena through observation and experimentation. The actions of a supernatural agent would become natural as soon as they came into contact with a natural world. The outside force would become a part of the closed system and it would be measurable.
We have no data to support the existence of this effect on anything that we measure. A god that does not affect the Universe in any measurable or significant way is not a god that is necessary. A god that does nothing does not need to exist.