It was enormously fluid, and no fully canonical version was ever established.

Some further threads that touch on the subject, in descending order of relevance. (NB: these are just the threads that I know of; I don't have records of threads I didn't participate in.)

• Was there retconning in ancient mythology?
• Greek "Mythology"
• How did Greek Literature influence Greek artwork?

Having said that, there were some efforts to -- not exactly come up with an authoritative version -- but to synthesise multiple traditions. The earliest exemplar is the Hesiodic Theogony (ca. 700-650 BCE), which attempts to synthesise a wide range of local traditions about individual gods into a single creation narrative. The Catalogue of Women (7th or 6th century) did the same thing for genealogical accounts of legendary mortals. From the fourth century BCE onwards we start to see a genre called mythography, which consists of encyclopaedic accounts of myths in summary form; the earliest ones weren't very influential, but ones from the 1st century BCE onwards have been extremely influential on modern mythological encyclopaedias, whether or not they were influential in antiquity. And when figures like Ephoros and Eratosthenes tried to put together unified histories of the (Greek) world, they began their chronologies with events that are to all intents and purposes myths (the Dorian invasion and the Ionian migration), slotting them into timelines that did indeed become authoritative for later historians.

So the real answer is no; but that didn't stop some people from trying.