1. In a medium bowl, stir sugar into 1 cup warm water. Sprinkle with yeast and let stand until foamy, about 5 minutes.
2. Whisk olive oil and 1 teaspoon salt into yeast mixture. Add flour and stir until a floury, shaggy dough forms. Turn dough onto a floured surface and knead until it comes together in a smooth ball that springs back when poked, about 2 minutes.
3. Transfer dough to an oiled bowl and brush it lightly with oil. Cover with plastic wrap and let rest in a warm place until dough has doubled in size, around 45 minutes. Punch down and cover again, letting it rise another 30 minutes.
4. Turn out dough onto a lightly floured surface. Divide into 2 equal pieces and allow to rest 15 minutes. Prior to grilling, stretch or roll each dough ball into a thin, 12- to 14-inch round.
NOTE: Dough can be prepared in advance. To store, refrigerate dough ball, covered, up to 2 days, or freeze for up to 1 month.