I believe the evidence is not to be found on some higher plane but on a more fundamental one. Science is based on a belief in a unversal order, a legacy of monotheistic belief but nothing to do with the scriptures. We find evidence for this universal order in the reliability of the laws science and the specificity of some fundamental constants.
The scriptures are irrelevant, and the evidence for this statement, is the remarkable discoveries made by Islamic scholars in the middle ages. Mathematics and astronomy, not to mention the discovery that the world revolved around the sun, were discoveries made in a civilisation founded on Islamic scriptures. But clealry scripture played no part in these discoveries. However what the Islamic scientists chared with their later Christian colleagues, was a deep conviction that the universe was subject to some sort of order, perhaps intelligence. Even Feyman joked that God must have been a hellover mathematician.
So Copernicus and Galileo and Kepler got there a few hundred years after the Arabs, not influenced by the Scripture of thier times, but a fundamental belief in some universal authority.
I think that the reason universal laws were never discovered in Eastern civilisations is because they do not believe that there is any universal authority. For the Buddhist believer the very nature of separate existence, as we know it, is challenged. All is inter-connected and there is no place for certainty is Buddhism, which is why it is quite happy to adopt Western theories of quantum mechanics.
To return to the orignal question, religion, as in the sciptures ( neither Christian nor Islamic) have no relevance to science. However, belief in an ordered universe is fundamental to it.