Most houses in ancient Europe, Asia, and Africa had thatched roofs. People have been thatching roofs since at least 10,000 BC, and maybe longer. Thatched roofs are hard to make, and you have to re-thatch them every few years or they will leak, but the materials are cheap and easy to get. You take dried grass or straw and make it into small bunches, and tie each bunch with a cord spunout of the same grass.
Here’s a video of a man in Ireland thatching a roof
Another problem of thatched roofs is that bugs and spiders and small animals like squirrels like to live in the roofs.
One advantage of a thatched roof is that it will gradually let the smoke out, if you have a cooking fire inside your hut, so you don’t need to build a chimney. Still, when people can afford it, they usually choose to have a baked clay tile roof, which will last longer and keeps out the rain better.