Graeber spends a lot of time arguing against exactly this assumption in The Dawn of Everything. I.e. that agriculture must come before civilization. Pretty persuasively, IMHO.
Besides these sites in Turkey, are there any places in the world where huge amount of rock was carved supposedly without agriculture to fuel the workers? The Stonehenge builders had agriculture, as did those who made the Easter Island statues. Agriculture built Egypt.
And if the site was occupied for hundreds of years, they could have been carved over time, spreading out the caloric requirements.
Even the idea of a hard binary between 'agricultural' and 'hunter gatherer' societies is put to the test, with evidence of civilizations that changed both locations and whole modes of culture and caloric intake seasonally.