Greek cosmogony has more than one starting point, and the theogonies that begin with Time are the ones that least resemble Hesiod. Pherecydes of Syros, writing in the sixth century BCE, is reported to have opened with three beings who always were: Zas, Chthonie and Chronos. His Chronos makes fire, wind and water out of his own seed, and from those the generations of gods proceed. The account survives in fragments and in later summaries rather than whole, so what can be said about it is limited by what the summarisers chose to record.
The Orphic theogonies go further. In the version Damascius reports from the Rhapsodies, unaging Chronos is a serpentine figure with the heads of a bull and a lion, joined with Ananke, necessity, whose coils wrap the whole of things. Chronos fashions an egg in the aether, and out of the egg comes Phanes, the first-born shining god, from whom the rest descend. Time here is not a measure applied to events but the maker of the frame within which events can happen at all.
That is a philosopher's cosmogony as much as a priestly one, and it was read as such early: the Derveni papyrus shows a fourth century commentator already treating an Orphic poem allegorically. Whether these accounts preserve early tradition or later systematising, and how much Iranian material stands behind the serpent bound with necessity, are argued rather than settled.