Dissolve the yeast with sugar in the warm water, and allow it to sit for 10 minutes, or until the mixture looks foamy and bubbly.
If using a measuring cup instead of a scale, spoon flour into the measuring cup and then level it off with the back of a knife. Add the flour and salt to the bowl of a stand mixer fitted with a dough hook. Alternatively, you can make this dough by hand, but note that the dough is on the sticky side.
Add the water and yeast mixture and 2 tablespoons of the olive oil to the flour mixture. Turn the mixer to stir, and allow it to mix until a shaggy dough is just formed. Turn up the stand mixer to medium for 5-6 minutes, or until a smooth, soft and elastic dough forms. It’s OK if it is a little sticky; if it’s not forming a cohesive dough at all, you can add a little more flour a spoonful at a time. Remove the dough from the mixer, gently form into a ball and transfer to a well-oiled bowl. Turn the dough in the bowl so that all sides have touched the oil. Cover the dough with a lightly oiled piece of plastic wrap, and then cover everything with a kitchen towel. Place the covered dough in a warm part of the kitchen and allow it to rise until doubled in size, about 1 1/2 to 2 hours.
Add 3 tablespoons of olive oil to a rimmed baking sheet. Punch down the dough that has risen in the bowl, then transfer it to the baking sheet. Gently press the dough into the edges of the baking sheet to form a rectangular shape, and flip it over so that both sides of the dough are equally covered in the oil. Press your fingertips deeply into each part of the dough, making dimples and helping the dough hold its shape. Cover the dough loosely with a well-oiled piece of plastic wrap. Let the dough rise again for 45 minutes to an hour. While the dough is rising again, preheat the oven to 425 F.
Before baking, top the dough with the olives, za’atar and a generous sprinkle of flake salt. Bake for 25-30 minutes or until golden brown with a crisp crust.
Once out of the oven, drizzle with more olive oil and allow to cool slightly before serving.