Short answer: Greek history, as opposed to myth and legend, begins about one hundred to three hundred years before the time of Herodotus.
Herodotus (c.484-c.425 BC) has been called "The Father of History".
he was the first historian known to have broken from Homeric tradition to treat historical subjects as a method of investigation—specifically, by collecting his materials systematically and critically, and then arranging them into a historiographic narrative.
The Histories is the only work which he is known to have produced, a record of his "inquiry" (ἱστορία historía) on the origins of the Greco-Persian Wars; it primarily deals with the lives of Croesus, Cyrus, Cambyses, Smerdis, Darius, and Xerxes and the battles of Marathon, Thermopylae, Artemisium, Salamis, Plataea, and Mycale; however, its many cultural, ethnographical, geographical, historiographical, and other digressions form a defining and essential part of the Histories and contain a wealth of information. Some of his stories are fanciful and others inaccurate, yet he states that he is reporting only what he was told; a sizable portion of the information he provided was later confirmed by historians and archaeologists.
Despite Herodotus's historical significance, little is known of his personal life.
The main persons listed as subjects of the history of Herodotus were:
Croesus (595-c.546 BC) King of Lydia.
Cyrus II The Great (c. 600-530 BC) The Great King, the King of Kings, The King of Lands and Peoples, The King of the World.
Cambyses II (d. 522 BC) The Great King, the King of Kings, The King of Lands and Peoples, The King of the World.
Darius I (c.560-486 BC) The Great King, the King of Kings, The King of Lands and Peoples, The King of the World.
Xerxes I (519-465 BC) The Great King, the King of Kings, The King of Lands and Peoples, The King of the World.
The battles that are main subjects include:
Marathon (490 BC).
Thermopylae (480 BC).
Artemisium (480 BC).
Salamis (480 BC).
Plataea (479 BC).
Mycale (479 BC).
Herodotus reports on the possible mythical origins of conflict between Europe and Aisa, but most of his work covers events in the previous two centuries or about 650 to 450 BC. It is likely that the sources used by Herodotus for recent events were more accurate that the sources used for earlier events that had more time for exaggeration, confusion, and propaganda during the transmissions of those stories.
The ancient Greeks began holding Olympic games every four years at Olympus in Greece. An Olympiad was the term for a four year period beginning the summer when Olympic games were held and ending in the summer at the beginning of the fifth year right before the next next set of Olympic games was held.
It eventually became the Greek custom to date events to the year of the Olympiad in which they happened, the first second third, or fourth year of the particular Olympiad.
Any event that was recorded at the time it happened as happening in a particular year of a particular Olympiad is precisely dated.
Timaeus of Tauromenium (c.345-c.250 BC) was the first historian to use Olympiad dating to date events.
The first Olympic games were probably held in 776 BC according to our modern Gregorian calendar.
And I believe that some ancient Greek historians considered that the age of myths and legends ended about then and the age of history began about then.
Therefore a rough rule could be that most Greek events said to happen before about 776 BC are myths or legends (though they could be true) and most Greek events said to happen after about 776 BC are more or less history (although possibly distorted or falsified history).