Stir the yeast and sugar into the warm water and let it sit 5 to 10 minutes, until foamy.
In a large bowl, mix the flour and salt. Add the yeast mixture and olive oil and stir into a shaggy dough.
Knead on a lightly floured surface for 5 to 7 minutes, until smooth and elastic.
Place in an oiled bowl, cover, and let rise in a warm spot for about 1 hour, until doubled.
Punch down, divide into 4 balls, cover, and rest 10 minutes.
Preheat the air fryer to 400°F (200°C) for 5 minutes. Lightly spray the basket.
Roll one ball into a 5- to 6-inch round, about 1/8 inch thick.
Air fry for about 2 minutes, until puffed. Flip and cook 1 to 2 minutes more, until lightly golden.
Repeat with the remaining dough. Brush with olive oil or butter and serve warm.