Science got started much earlier than you think.
Consider the example of the sphericity of the earth:
“There never was a period of ‘flat earth darkness’ among scholars (regardless of how many uneducated people may have conceptualized our planet both then and now). Greek knowledge of sphericity never faded, and all major medieval scholars accepted the earth’s roundness as an established fact of cosmology.”
~ Stephen J. Gould, Dinosaur in a Haystack (New York: Three Rivers Press, 1996), 42.
That statement is undisputed by scholars of ancient and medieval history.
Then there’s heliocentrism.
Aristarchus of Samos (310-220 BCE) maintained that the earth rotates on its axis and revolves around the Sun. That view was eclipsed by Ptolemy’s geocentric system for centuries, in part because the latter had more effective means of calculating and predicting the motions of heavenly bodies. The other reason was that some philosophers, such as his contemporary Cleanthes the Stoic, thought such an idea “impious.” So centuries before Christianity, you could find people offended by the suggestion that the Earth is not the center of the universe.
But heliocentrism was never entirely forgotten. The 16th-century priest who re-introduced heliocentrism to Western Europe, Nicolaus Copernicus, made notes about Aristarchus but was prudent enough not to include them in the published version of his work De Revolutionibus Orbium Coelestium (1543).
And then there’s evolution.
That idea also finds clear precursors in ancient Greek thought. The Internet Encyclopedia of Philosophy says:
“Anaximander is often regarded as a precursor of the modem theory of development. He deduces living beings, in a gradual development, from moisture under the influence of warmth, and suggests the view that men originated from animals of another sort, since if they had come into existence as human beings, needing fostering care for a long time, they would not have been able to maintain their existence. In Empedocles, as in Epicurus and Lucretius, who follow in Hs footsteps, there are rudimentary suggestions of the Darwinian theory in its broader sense; and here too, as with Darwin, the mechanical principle comes in; the process is adapted to a certain end by a sort of natural selection, without regarding nature as deliberately forming its results for these ends.”
My checking of sources has not revealed any serious dispute about that from specialists either.
It’s well known that the Islamic world between the 9th and 12th centuries was awash in science and scholarship; for instance, it’s where Europeans learned the system of “Arabic” numerals, which is far more efficient than the old Roman-numeral system.
But even the Christian Middle Ages, often thought of as the pinnacle of obscurantism, saw significant scientific developments. You can read about them in James Hannam’s book The Genesis of Science: How the Christian Middle Ages Launched the Scientific Revolution, a copy of which I own.
Finally, it’s often thought that the Chinese, who invented explosives nearly two millennia ago, never employed them for anything more useful than firecrackers. But that isn’t true either.
So why did the so-called “scientific revolution” take off so relatively late in human history? Apparently, it just took a long time for various developments to reach critical mass.