The “gospels were dictated by first hand witness” idea is a massive problem because that’s not first hand account at all, that’s actually someone claiming that someone else told him “dude I swear I saw it happen in front of me as clear as I see you” (or worse, the guy who wrote it claims that he found this text written by someone else 50 years ago) and we somehow chose to believe both the guy who wrote it and the supposed guy who told him that. Having something dictated is second hand account, not first hand, because that’s just changing the pronoun of the person speaking. And there were extensive analysis of the text itself to try to figure out what kind of person would have phrased this or that in certain ways, whether it says “I saw that myself” or “my uncle who works at Nintendo told me he saw it himself”, and that analysis, done for the entirety of the Bible, has gone pretty far, including the gospels. As far as I know about it, the biggest point about that analysis is which gospel was written first and which ones copied from which ones or added their own thing, rahter than 4 different people recounting their memories of the same events.
I don’t know about the timeline of the temple; I’ve heard it brought up before, but I haven’t heard that it was considered conclusive evidence for dating the text, so I don’t know more than that and how it holds to the text analysis.
Sumerian culture was many thousands of years after the end of the ice age. Even the last big cooling event was a couple thousand years before Mesopotamian cities, and that was just a cooling event, not something with big ice sheets that turn into floods when it warms up. What they had is the Tigris and Euphrates that did flood on a regular basis, sometimes catastrophically - the floods of the Nile brought fertilization from the upper terrains they covered and it was predictable like clockwork, but the floods of Mesopotamia were destructive and unpredictable. One thing it absolutely didn’t do is cover the whole Mesopotamian plain, it just flooded the land surrounding the river. Unfortunately, people make cities near those rivers - but the mountains were WAY too far to run to them. Mesopotamia is just basically one gigantic flat plain, it doesn’t have random mountains in the middle.
We have geological records of one big flood dated around 2900 BCE that destroyed most notably Shuruppak (it got better), which held a big cultural position at the time, and a few other cities in the area. What’s funny is that by the time the Flood story was integrated into Akkadian / Babylonian culture, sometimes between 2000 and 1800 BCE, there were still people living in Shuruppak, which is named in those myths as having been destroyed.