Homer knew about them in the “dark ages”, since he included them in his famous poems. But that was before the big Greek civilization came into existence. Where and when did Greeks create myths about their gods?
There's not one single moment when a myth forms. They are much more fluid than that, and there is lots of evidence that much of what we know as Greek myth has evolved from older, Near Eastern myth.
A classic example is the Hurro-Hittite myth of the succession of Alalu–Anu–Kumarbi, which resembles very closely the succession of Ouranos–Cronus–Zeus. The motif of castration is prominent in both myths, for example, as is the motif of a god swallowing his children in order to be overthrown, and so on. It's clear that the Greek myth either derives from Hurro-Hittite one in some way, or that both the Greek and the Hurro-Hittite myths derive from an even older ancestor – but it'd be hard even in theory to point to a single moment in time when the Greek myth was 'created'.
Another myth that appears across the ancient Mediterranean is the idea of the Great Flood, which is famous in Greek mythology from the figure of Deucalion, but also in Hebrew mythology with the figure of Noah. The Sumerians also had the concept of a Great Flood: the Sumerian King List divides its history into pre-Flood and post-Flood periods.
The other thing to mention is that myths continued to evolve even when they had reached their apparently canonical form in Homer. This might be as simple as a change in what someone is called. In the Odyssey, for example, Oedipus' wife is known as Epicaste, whereas in Sophocles' Oedipus the King she is known as Jocasta. Maybe there were multiple names for the same person floating around? Or maybe there was a single name that evolved in the couple of centuries between 'Homer' and Sophocles.
There might be bigger changes. In Aeschylus' Oresteia, for example, one of (if not the) key event is the sacrifice of Agamemnon's daughter Iphigenia in order to appease Artemis and allow the Greek army to sail to Troy. In the Iliad, not only is Iphigenia apparently known as Iphianassa, she is apparently not dead, but alive and well back in Troy, since Agamemnon offers her as a wife to Achilles. That's a pretty big difference!
One way of thinking about this question is when do these myths become specifically Greek, and your answer to that might be when the gods start being called by their Greek names – e.g. Zeus, Poseidon, Athena, etc. What's interesting about this is that the names of the Greek gods appear to be older than the Greek language. The name 'Poseidon', for example, appears in the proto-Greek language of Linear B (both as Po-se-da-o and Po-se-da-wo-ne). So if a myth is 'Greek' is it contains Greek names, we are already looking back to way before the composition of the Homeric poems, to the Minoan period of the mid-2nd millennium BC. But it really depends on what you think makes a Greek myth Greek.