In a large mixing bowl or stand mixer bowl, combine warm water, yeast, and sugar. Stir gently and let sit for 1–2 minutes until foamy or bubbly, indicating the yeast is active.
Add all-purpose flour and salt. Mix with a dough whisk, spoon, hand, or dough hook until the dough is lumpy and sticky. Scrape down sides as needed.
Cover the bowl and let the dough rest at room temperature (about 75°F) for 30 minutes.
Wet your hand, stretch one side of dough upward, fold over the center, rotate bowl, and repeat 4 times. Shape into a ball.
Transfer dough to a lightly oiled container, cover, and let rise for 1 hour 30 minutes at room temperature.
Preheat oven to 500°F.
Lightly dust pan with semolina flour. Rub olive oil on hands to prevent sticking.
Press dough into a flat round, then stretch to 10–12 inches using backs of hands or knuckles, keeping air bubbles intact for an airy crust.
Add pizza sauce, shredded mozzarella cheese, and toppings.
Bake for 10–15 minutes, or until crust is golden brown and cheese is bubbly.
Cool slightly before slicing and serving.