Almost certainly not. We are still understanding how far back settled people go. There is strong evidence of at least 9 sites that go way back, the people that built Gobekli Tepe were likely 11K years ago, Jericho looks to have been continuously settled at least 9,0000 years ago, there is a site in the Galilee (Ohalo II) that appears to have been settled around 23,000 years ago.
The issue is that when you start looking for archaeology that far back the evidence just becomes really hard to find. Pretty much only stone would survive, anything made out of wood would be gone, unless it was preserved in a very specific manner and then we just happened to find (such as we did with the
Kalambo structure, which is mind boggling) .
The real question is what is a "civilization"? Personally I lean towards a more liberal definition allowing for settled groups of people to be a "civilization". The definition has previously been based around domestication of plants and farming; but that's really rather narrow of an idea, but that's largely where the 6,000 years ago comes from. There is no reason you can't have a "civilization" built around pastoralism and or/hunting, fishing and gathering certain foodstuffs.
Certainly the people getting together in the area at and surrounding Gobekli Tepe were even more than that as we discover more about the site. Right now we only have less than 10% of the site excevated and it has changed all thought on how old some of these sites may be and how advanced the people that made them were.