Halcon: The lengthy and rather scientific process you theorized
Oh, I don't think it was scientific at all. Which is one reason why it would take so long to develop. I am not talking about a group of nomads hashing out the cause of lightning over a few evenings and coming up with a long explanation. Even today, we have a tendency to jump to conclusions on insufficient evidence in order to deal with things we may not understand. This trait would likely have been dialed up in a time when every bush might harbor a nasty surprise and getting a small cut might be catastrophic. I'm talking about ideas that probably took generations to begin to take shape, and in decidely non-scientific ways.
Again, if there was a god who interacted with these people and guided them at some point, the development of religion would have begun along a single and clear track. With the certainty of god as a starting point, the answers would not have been made up or random. And, presumably, those humans would have had answers to questions about lightining and infections that would have stood the test of time. Their approach was not scientific or methodical. It was reactionary and driven by fear and a need to have an answer immediately, even if the answer wasn't accurate.