Anthropologists studying the Aborigines in Australia made a pretty startling discovery a couple of yeas ago, a description within their oral history of an erupting volcano, complete with its location. That volcano erupted close to 40,000 years ago. They didn't build empires or more than a couple of city states, but you can't deny their civilization.
https://www.science.org/content/article/aboriginal-tale-ancient-volcano-oldest-story-ever-told
We also know that the civilization that produced Gobekli Tepe was thousands of years older than Ur, and the founding of Jericho dates to the same period. In addition, there is some suggestion that Ur was founded as a trading outpost for another civilization, as fragmented history from the region describes god-men arriving by sea from the south. Deep time gets murky fast.
I have to give the Sumerians their due, they came up with math, astronomy, physics, and other things we're just catching on to. However, they weren't the most ancient civilization, not by at least 5,000 years. In addition, we have no idea what could be drowned, buried, and long forgotten on continental shelves that were exposed and likely habitable during the Ice Age(s).
Interesting article, though.
I also disagree about irrigation being a hallmark of civilization. You can't deny the Aztecs were civilized (although I'd never have wanted to live there). Their strategy was to build floating islands out of wood and woven mats to sit on top of the water, the plants growing in a shallow layer of soil and watered from below. It was more hydroponics than irrigation, a novel solution that worked well enough to feed their city.