Stonework was used for major public works projects back then. It was expensive. Things like temples, aqueducts, government buildings, city walls. Common people built using brick, and plastered it with actual plaster, or clay mud painted with whitewash for a bit of waterproofing. Peasants built huts of wattle and daub: a basketwork frame of poles and interwoven branches or reeds, covered with that aforementioned clay mud. Sometime whitewashed, sometimes not. Roofs on more substantial buildings were tile, on less expensive buildings thatch.
Flat roofs extended the living space: brick walls absorb a lot of heat in the summertime, keeping the interior a bit cooler than outside during the day, but at night, the walls radiated that heat, so people went to the roof to sleep, where it was cooler. A peasant’s wattle and daub wall didn’t absorb much heat (lots of straw in the clay mud plaster) so they didn’t need, and couldn’t afford, a cool rooftop sleeping space. Thatch roofs for them.