All of the mythical figures and heroes like Heracles, Jason, the Trojan War, etc. are set during the Late Bronze Age (1600-1100 BCE). The classical Greeks of the fifth century bce looked back to the Bronze Age as an Age of Heroes, which came to an end when Zeus forbade the gods to mate with mortals, marking the beginning of the Iron Age. Obviously these are stories, but often they have a kernel of truth to them, the Trojan War most likely didn't happen the way the story goes, but there definitely was a Troy and it really was destroyed (a number of times throughout its history). The Seven Against Thebes recalls the destruction of the palace of Thebes, which really was destroyed around 1200bce. So the Greek were looking at there mythical past because of the oral tradition that passed these tales down through generations, but they were also surrounded by evidence of the Bronze Age, they could see the ruins of the palaces of Mycenae and Tiryns or the Bronze Age wall that still exists on the Acropolis in Athens.

But the Greeks lived in the shadows of the Near East and Egypt, they knew these cultures were older and that they had influenced Greece. Kadmos is a Greek hero who was thought to have came from Phoenicia (Lebanon) and brought the alphabet to Greece. Emulation of Near Eastern culture had been fashionable among the elite of Greece in several periods, in the Bronze Age elites traded for items from the East as far off as Afghanistan to show off their status, and in later Greece it was not uncommon for Greek expats to take up residence at the court of the Persian king.

It's a really interesting question and I wish I could write an entire paper on it, because the Greeks saw that their culture had many influences from other cultures, the Mycenaeans and Minoans of the Bronze Age, they believed Dorians swept into Greece after the Bronze Age ended and introduced other cultural aspects, and the Near East influenced them politically and culturally.