Sure, but the notion that hunter-gatherers built something as large and complex as Göbekli Tepe seems unlikely. Construction required a sustained effort by expert craftspeople over many years. They would have needed a higher level of organization and more surplus resources than primitive hunter-gatherers could sustain.
I mean, I think this is part tautological because you've defined them as primitive and not craftspeople. Couldn't they be non-primitive but largely nomadic craftspeople?
(Gokebli Tepe in particular has evidence of processing of grains, but not large scale farming of them, and they might have only settled there for part of the year.)
How exactly could nomadic people develop advanced masonry skills? Are there any proven examples of nomadic people building large, complex permanent structures? What were all the architects and construction workers eating at the job site?
"How exactly could nomadic people develop advanced masonry skills?"
By being half nomadic. When you move around and set up camp often and build temporary structures out of wood, there is opportunity to learn masonry.
And when you often visit the same places, and evertime you add something permanent and more lasting, then specialists will develope.
Nomadic people were usually not changing place everyday. They changed places, once the game in the area were exhausted or the temperature became too cold/warm. But next year, they come back to a good spot. And so over the years important spots can get sophisticated buildings.
There are thousands of remnant river and ocean rock walled fish traps all across Australia, some were very large and they all received a bit of annual touch up and modification for thousands of years .. until Europeans with river boats blasted many to clear passage and pushed off their traditional owners to reservations or worse.
Or maybe your assumptions about agriculture/surplus/specialization are wrong. I'd start by digging deeper into existing evidence instead of evidence free speculation of complex agricultural societies lost to time.
