Neolithic behaviors differing from the modern familiars are all interesting, but when we use the word "civilization", we are definitively talking about cities. Associating onset of civilization with 3-4000 BCE is a conclusion from present evidence, not a definition, and would need to be changed in the face of new evidence of cities.
Hints at civilization pre-4000 BCE typified by GT are as interesting as other neolithic phenomena. To be clear: while it is possible, in principle, that GT builders invented all their stonework methods de novo, it is clearly much more likely that they drew on a long history of gradually more sophisticated stonework not yet unearthed, possibly elsewhere. What we know about sea level changes allows that much of such evidence may now be under water, although it could also be found in the Tepes yet to be excavated.
We have absolutely no reason to believe that areas now deluged were unoccupied, or that the people who lived in those places chose to stay there and drown. They would have brought their culture uphill with them.
The entire Persian Gulf was recently dry land. Australians retain oral records of the social upheavals when people who lived in the Sahul region between present Australia and New Guinea were obliged to move uphill, to where other people already lived. Similar upheavals must have occurred on the present Indonesian islands and nearby peninsulas, absorbing influx from the hundreds of thousands of square miles of the the now deluged Sundaland.
People 6000 years ago, or 11,000 years ago, were no more clever than 20,000 years ago. What was evidently done 6000 years ago could have been done longer ago, given only population density and surplus food production. Undiscovered civilizations are certainly possible: the huge Amazon basin civilization was entirely unsuspected only decades ago.