Stir warm water with sugar and yeast; let foam 5–10 minutes.
Add flour, salt, and olive oil; mix into a shaggy dough.
Knead on lightly floured surface until smooth and elastic, 8–10 minutes.
Grease bowl, add dough, cover, and let rise until doubled, 45–60 minutes.
Heat oven to 475°F with a baking stone or inverted sheet on middle rack.
Punch down, divide into 8 pieces, and roll each into a tight ball.
Cover and rest 10 minutes to relax the gluten.
Roll balls into 6-inch rounds, about 1/4-inch thick; dust with flour if sticky.
Bake 3–5 minutes until puffed and lightly golden; work in batches.
Transfer pitas to a towel-lined basket to stay warm and soft.