You're correct that science began "exclusively within the Western civilizational orbit." However, the Greeks -- Euclid, Aristotle, Archimedes, Eratosthenes, etc. -- who were undoubtedly the originators of what we call science, were neither Jewish nor Christian. The West didn't become Christian until the early 300s (AD). Western Civilization was flourishing for at least six centuries, probably seven centuries or more, when the prevailing religion was worship of the Olympian gods. Paganism.
But poor ol' Zeus just can't get any respect these days.
Of course, they were followed by the Geeks
(that's me a little to the right).