What led to Ancient Greeks to create such a fascinating history and culture?

It’s a good question, and a question that has been posed and discussed by many before.

• The history of Classical Greece is more interesting than that of other places, because it had more conflict and more players: it wasn’t a steady-state, stable empire. (That came later, with the successors of Alexander.) Of course, being more interesting does not correlate to being happier.
• The history of Classical Greece has gathered more interest, because its historians were read more; its historians were read more, in turn, because its culture was so fascinating to its successors. There’s nothing intrinsically more interesting about the Peloponnesian War than any number of other conflicts in antiquity—except that the Peloponnesian War had its Thucydides.
• A key reason Jared Diamond identified for the West gaining technological supremacy was that it was decentralised, featuring a lot of small states in competition with each other during the Renaissance. You can say the same about Classical Greece, and I’m sure people have: lots of small city-states, acting as different laboratories of government and culture and technology, promoting trade and cultural exchange because they were not self-sufficient, and competing with each other.
• When we think Classical culture, we mainly think Athens. Athens prevailed for a small time (but a critical time) because it got its own informal empire going, it was open to immigrants (though it did not grant them full civic rights), it had confidence in its power, and its dramatists and philosophers had enough leisure to ask tough questions. Athens did not come out of nowhere though: it built on centuries of both its own political experiments and others’. And remember that much of the science of Classical Greece came from Ionia, which was much more comfortable with the Persians.
• As I’ve said elsewhere, a major reason why the West finds Ancient Greek culture fascinating is that it traces its intellectual heritage back to Greece. It does so, because Rome does so. Rome did so, partly because of its direct contact with the Greek colonies in Italy, but also, and likely more so, because of its contact with the Greek Empires of Alexander’s successors, the Seleucids and Ptolemies and whoever it was that was running Greece. Politically, these empires were nothing to do with Athens and Sparta; but Athens and Sparta and Ionia is where they drew their culture from.