Add lukewarm water to a large bowl. Sprinkle the yeast over the water, then the sugar. Set in a warm spot and let it sit for 10 minutes, or until the yeast starts to bubble.
Once your yeast is bubbling, add the olive oil, flour, and salt to the mixture. Stir with a spatula to combine until the mixture is cohesive and too sturdy to stir any longer.
Carefully transfer the dough to a flat and lightly floured surface. Knead the dough until a smooth ball is formed—about 3-5 minutes. The dough should be a little sticky to touch. Place the dough ball into a bowl and cover with a dry dish towel. Place the bowl in a warm spot and let the dough rise for about 1.5-2 hours, or until it has double in size.
Once the dough has risen, bring an oven rack to the upper mid part of the oven (in most ovens, this will be the second insert). Set a pizza stone on the rack. If you don't have a pizza stone, simply line two baking sheets with parchment paper and set them aside. If you're using a pizza stone, you'll want to preheat it in the oven for 30 minutes; baking sheets don't need this treatment.
Transfer the dough to a flat and lightly floured surface again; divide the dough into six pieces. With a rolling pin, roll each section into an oval, just until the dough resists and pulls back. When this happens, set that piece aside and move on to the next. Repeat this for all sections of dough.
When the oven is ready, take a section of dough and roll it once more bringing it to about 12 inches long and 4 inches wide. To prevent sticking, you can add a bit more flour to your flat surface or rolling pin; flip the dough over a few times to make sure it isn't sticking.
Slather the dough with a layer of the za’atar mixture, about 1.5 TBSP per oval, leaving about 1/2 an inch of empty space around the edges so you have a crust.
Carefully transfer the dough to the pizza stone, or baking sheet lined with parchment if using going that route. Repeat with the other dough sections and bake until the crust is golden brown, about 7 minutes. I was able to fit two flatbreads on my pizza stone at a time, so I baked them in pairs.
Once the flatbreads are golden and bubbling, remove them from the oven. If you're using a pizza stone, you'll want to use a pizza scraper. Serve warm with your choice of topping and dips.