I'm not sure I understand your question entirely, but it seems to draw on a misperception: the texts that preserved the mythologies of the ancient world drew on oral traditions that pre-existed and usually co-existed with the documentations of those narratives and beliefs. There was not a phase when people experienced the stories about "the gods" in the present, "in real time," and then later recounted them in the past tense, only to have them be eventually preserved in writing.

For the most part, these oral narratives are what folklorists would refer to as legends: stories told generally to be believed. They fall into several varieties: etiological legends that explain the origin of things; general legends that recount the affairs of supernatural beings, and historical legends that were set in specific times in the past. Even with this last time of legend, people did not necessarily live at a time when the proto-events occurred. Like most legends, there were not necessarily events that inspired the narratives.