From the beginning of the period you said, ancient greece, they already had lots of alternative explanations for what they saw in daily life. Atomism like I said for example. That's back in the 5th century bc. India had something similar to atomism around that time too. Before that there were explanations for natural phenomena like lightning, earthquakes, the sun, etc without gods. Maybe those ideas weren't more talked about because of connections to atheism and the risk of death or exile. Or maybe it was more difficult to spread those ideas because they didn't have the practical applications they have today. So it didn't matter much if gods were doing things or if it was something natural. But choosing to believe the more complicated explanation of gods doing things needs faith.