This question has a few subtleties. For one, what do we mean by "advanced"? Advances in what? Technology? Politics? Culture?
Technologically, the Greeks were not much further advanced than the other societies around them. Or maybe they were; it is hard to know for sure. The Athenians certainly advanced architecture and had a very "advanced" navy for the time. Other things are also interesting technologically. The aeolipile, otherwise known as "Hero's engine" (because it was described by Hero of Alexandria), was essentially a primitive steam engine. And then there's the antikythera mechanism, a kind of ancient Greek computer which allowed for elaborate astronomical calculations. It was found by archeologists in the early twentieth century.
But these were exceptions. Where the Greeks truly advanced civilization was in the realms of politics and philosophy. Athens witnessed the first participatory democracy in the world, and rhetoric and philosophical thought experienced tremendous advances...
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