I just don't think it's as simple as that. The 'scientific method' didn't just appear one day, as a sudden revelation. Indeed it seems more a retrospective rationalisation of what people had been doing for some time without consciously deciding on it.
To start thinking in a 'scientific' way requires all kinds of intellectual and physical preconditions. Religion was one of the things that created those conditions.
I can't really sustain an argument over it because I've forgotten all the things I read about it in the past (like climbing a ladder that then falls over leaving you wondering how you got here, I just know I at some point decided I didn't agree with what you say here, even if I don't quite know why any more).
Besides, while I know I'm not being at all convincing, it doesn't seem that important an issue given where we are now. It's a matter for historians, really.
For any and all of religions help in advancing science it has done far worse in holding it back. Take Islam for example, at one point they were the absolute pinnacle of scientific discovery during their golden age. Then the religion changed and after that the scientific advances made by Islamic people literally fell off a cliff. We are talking billions upon billions of people taken completely out of the realm of science around the 13th century and with very few exceptions they have yet to recover. It has to be among the largest travesties in scientific advancement in our history. Muslims make up almost a quarter of the global population and yet have earned only 1.4% of Nobel prizes. It is impossible to even imagine the number of Newton's, Einstein's, and Tesla's (Nikoli not Musk) that were taken out of the scientific pool because of religion.
So yes, you can show many scientific discoveries that were helped by religion but how many geniuses and truly great scientific and mathematical minds were kept out of their respective fields because of religion? Obviously that is a number that is impossible to prove but one can only fathom the truly greats we have lost and that is just one example.