I'm afraid they do not. It should be noted that even the Hebrew scriptures, probably the only ones I can think of that has a date of creation so closely tied to generations of men, is not really precise, for a generation is not a precise number.
However, some ancient Greeks did try to come up with dates for certain mythological events, particularly the Trojan War. Herodotus said that it was 800 years before him (= ca. 1250 BCE), and connects it chronologically to Heracles, Dionysus, and Egyptian mythology.
Among the Greeks, Heracles, Dionysus, and Pan are held to be the youngest of the gods. But in Egypt, Pan is the most ancient of these and is one of the eight gods who are said to be the earliest of all; Heracles belongs to the second dynasty (that of the so-called twelve gods); and Dionysus to the third, which came after the twelve.
Herodotus, Histories 2.145.1
These are Egyptian gods here, rather than Greek ones. Their equivalents are as follows:
- Dionysus = Osiris
- Heracles = Khonsu (?)
- Pan = Min
How many years there were between Heracles and the reign of Amasis, I have already shown; Pan is said to be earlier still; the years between Dionysus and Amasis are the fewest, and they are reckoned by the Egyptians at fifteen thousand.
Hdt., Histories 2.145.2
Here he is referring to his earlier chronology, all Egyptian still, which I'll discuss after this passage.
Now the Dionysus who was called the son of Semele, daughter of Cadmus, was about sixteen hundred years before my time, and Heracles son of Alcmene about nine hundred years; and Pan the son of Penelope (for according to the Greeks Penelope and Hermes were the parents of Pan) was about eight hundred years before me, and thus of a later date than the Trojan war.
Hdt., Histories 2.145.4
We know he has shifted back to Greek chronology by not only reversing the chronology of the Egyptians (and reversal is a very Herodotean thing to do; see Hartog's book at the botton), but listing the Greek parentage. Since Herodotus' life was roughly 480s to after 420, I'll round to roughly 450 for his "time". That gives us 2050 BCE for the god Dionysus (though this would conflict with Euripides!), 1350 for the life of the hero Heracles, and 1250 for the god Pan, which puts the Trojan war roughly around 1300-1275 or so. This is pretty consistent, as Heracles sacked Troy before Agamemnon, and after doing so put child Priam on the throne. Priam, of course, was an old man during the Trojan War (Apollod. 2.6.4, 3.12.3).
Now, the passage Herodotus mentioned above I reproduce below (and can be found at 2.43):
Concerning Heracles, I heard it said that he was one of the twelve gods.
Side note: The Egyptians had different pantheons depending on what city you were in. There were either a set of eight (the Ogdoad of Hermopolis: Nu and Naunet, Amun and Amaunet, Kuk and Kauket, Huh and Hauhet), set of nine (the Ennead of Heliopolis: Atum, his children Shu and Tefnut, their children Geb and Nut and their children Osiris, Isis, Set, and Nephthys), nine plus one (centered in Memphis, based on the Ennead but with Ptah as the head), or a set of twelve, of which I do not think we know very well.
But nowhere in Egypt could I hear anything about the other Heracles, whom the Greeks know.
Another side note, this Heracles is actually the Phoenician god Melqart. See Bonnet below if you know French and have access to a scholarly library, or Google Melqart and you can probably find some good information. Or ask another question here!
But Heracles is a very ancient god in Egypt; as the Egyptians themselves say, the change of the eight gods to the twelve, one of whom they acknowledge Heracles to be, was made seventeen thousand years before the reign of Amasis.
Amasis here is Ahmose II, who was Pharaoh 570–526 BCE, placing Heracles in Egypt to ca. 2250 (rounding to a nice middle number), which would make it in the middle of the 6th Dynasty.
Herodotus, of course, was not the only historian to work out dates for various mythical events, and Wikipedia has a nice list of various Late Classical/Hellenistic scholars' dates for determining when the Trojan War happened:
Ephorus gives 1135 BC, Sosibius 1172 BC, Eratosthenes 1184 BC/1183 BC, Timaeus 1193 BC, the Parian marble 1209 BC/1208 BC, Dicaearchus 1212 BC, Herodotus around 1250 BC, Eretes 1291 BC, while Douris 1334 BC.
There is one further clue about the "origin" of the Greek world, but it is even more imprecise:
Hecataeus the historian was once at Thebes , where he made a genealogy for himself that had him descended from a god in the sixteenth generation. But the priests of Zeus did with him as they also did with me (who had not traced my own lineage). They brought me into the great inner court of the temple and showed me wooden figures there which they counted to the total they had already given, for every high priest sets up a statue of himself there during his lifetime; pointing to these and counting, the priests showed me that each succeeded his father; they went through the whole line of figures, back to the earliest from that of the man who had most recently died. Thus, when Hecataeus had traced his descent and claimed that his sixteenth forefather was a god, the priests too traced a line of descent according to the method of their counting; for they would not be persuaded by him that a man could be descended from a god; they traced descent through the whole line of three hundred and forty-five figures, not connecting it with any ancestral god or hero, but declaring each figure to be a “Piromis” the son of a “Piromis”; in Greek, one who is in all respects a good man.
Herodotus, Histories 2.143
Hecataeus was Herodotus' real predecessor. He wrote genealogies of the world, including Greek myths, and it's a shame we do not have it anymore, otherwise we might know a bit better when he thought the world began.
Anyway, this passage clues is in on two things. One, Hecataeus places humankind sixteen generations back. This is difficult to reckon, because we do not know how many years he was counting as a generation, but by a normal 40 years, it leads us to 1140 (from 500, when Hecataeus was already a grown man, so perhaps even earlier). This is unlikely to be exactly the case, as he must have placed the Trojan War around this time, as Herodotus did. An alternative would be that he merely placed his line back that far, assuming that the gods were still reproducing with mortals, and Herodotus (and this unnamed Egyptian) must just be mistaken in his assumption that that's when the gods were mating in the beginning.
The other thing it lets us know is that the Greeks could imagine that humans were around 10800–14250 BCE (i.e. 10,350 to 13,800 years before their time).
That must have been pretty outrageous to the poets!
Bonnet, C. 1988. Melqart. Cultes et mythes de l'Héraclès tyrien en Méditerranée. Leuven.
Hartog, F. 1980. Le miroir d'Hérodote. Essai sur la représentation de l'autre. Paris.
-- Translated in 1988 as The Mirror or Herodotus: Representations of the Other in the Writing of History by Janet Lloyd. Berkeley/Los Angeles.
How, W. W. & J. Wells. 1928. A Commentary on Herodotus. 2nd ed. Oxford.
Linforth, I. M. 1926. "Greek Gods and Foreign Gods in Herodotus." University of California Publications in Classical Philology 9.1: 1–25.
Harrison, T. 2000. Divinity and History: The Religion of Herodotus. Oxford.