In my opinion, in ancient times before science method discovered, people didn't know the scientific principle behind inventions, nor could they use it for new invention, thus most ancient inventions were made randomly by luck or accumulated life experience, hence size of population and interactions in trade help.
After science discovered by Europeans, inventions exploded exponentially, that's why the west dominate the world since then.
This is why I emphasize on ancient Greek's Euclid's Elements, their deductive method is the key, without it, science couldn't be discovered.
No matter how many inventions by Sumerians/Egyptians/Indians/Greeks/Chinese, those specific inventions can't lead to modern science, only theory like deductive method can