The approach is naturalism (I’m referring to the view that all things are natural, that there exist no supernatural reasons nor causes) is testing for something in the laboratory in controlled conditions when all is being watched. It is a subset of all that happens outside and can only be a good representation given the assumption that whatever is in question behaves the same in the laboratory as outside.
Imagine a village with a rain forest bordering it. The villagers can measure the existence of rain by putting cups outside. Rain is simple and consistent and this experiment works fine.
But trying to prove directly God via the means of science? This cannot be done inherently by the limitations posed by the “consistent assumption” of naturalism. God is not like rain that falls dumbly in the same way both inside and outside in the village. Rather He is like a tiger that lurks in the jungle beyond the village, who strolls close to the village when he pleases. The the villagers that insist on a strictly naturalistic explanation for all things like villagers that dig holes in plain view randomly all over the village and outside of it to prove the existence of the tiger. If a tiger is found in them then tigers exist. If no such thing ever falls in the neatly made holes then tigers do not exist.
Why should God have to oblige humans to prove his existence. Who is God then, you or Him? He does as he pleases, he does not have to fall in your hole to exist. How silly we humans can be at times.