Those places that were destroyed almost certainly didn’t have things older than Ur, Akkad, Nippur, Uruk. They would have had works from the periods before it, but just the Old and Middle Babylonian and Assyrian periods, not much more than that. Writing beyond religious centers was spread across Mesopotamia starting the Ur III dynasty then the Old Babylonian period, reaching to the end of Anatolia, so there wouldn’t have been a prolific writer like an ancient Tolkien or GRR Martin before Enheduanna in Akkad. We can actually pinpoint when writing began and when it spread, so we’re pretty sure there can’t have been anything big written and lost older than that. Because very few people knew how to write before Ur III, and these people simply weren’t writing epic stories, they were writing accounting receipts and religious praises, and that peak was Enheduanna. It’s only during the Ur III dynasty and then the Old Babylonian period that people started writing the stories that were popular outside temples.

What was lost in the big collapses, when it comes to stories, would be smaller individual texts, variations and extra details of texts we know, not entire bodies of work completely lost everywhere - and they would be texts written well after Ur III. Any big work that existed in that period would have spread everywhere during the multiple empires that came and went, and there’s always a place where fragments survive - if only because the place was lost and buried (not destroyed) before the various collapses, and only resurfaced in modern time. We knew about the Sumerian traditions without knowing what they were or that Sumer even existed until the 19th~20th century, because those stories survived through other cultures, starting with the Old Testament, and Greek myth, and then we found out that Gilgamesh and Atra-hasis predated them all, and we figured out when THAT turned from oral tradition into writing, and then from a handful of individual texts into a single epic. Because they weren’t actually destroyed - they were just buried. The bigger works that were lost in the various collapses and burnings from the Sea People to Alexandria, and weren’t already copied somewhere else would be texts of sciences, records, philosophy, that didn’t have a wide cultural impact beyond the capital - so not epic stories, and not older than Ur III.

So obviously, before writing was invented, we can only speculate so much on what existed. Surely there were people who had stories before all that, and not just in Mesopotamia, Europe and Asia obviously had their own cultures and stories, but that would have been oral tradition only, and when the culture dies without ever being written, the story is lost. We can actually take some guesses at the most distant roots of the dragon myths and some constellation stories, but we can’t guess into existence an epic from before writing was invented.

After writing was invented, there weren’t any stories written for a long time until the big empires, so nothing before Akkad, Ur III, and the Old Babylonian period. Even in other places where writing existed the earliest, it turns out that what they wrote didn’t include stories until relatively late (looking at you, Harappa and China’s Shang dynasty). The rare people who knew how to write simply didn’t write stories, they wrote religion and accounting mostly. It only begins with the Ur III texts, which is Gilgamesh (also the Enmerkar-Lugalbanda cycle that never made it to the same level of popularity).

After writing was spread across the Mesopotamian empires, there’s very little room for something that was entirely lost everywhere, there’s always a place where fragments survive and other cultures pick up on it. We have the Baal cycle in Ugarit, we have Greece, and then we have the Old Testament. Anything that could be truly lost and not just buried would be paper (and adjacent), much later, and wouldn’t have anything older that doesn’t already appear somewhere else. The odds of an entirely unknown, big enough story, existing before and disappearing in that period, are not very significant. If it existed, it spread into something else that survived.