In a large bowl or stand mixer fitted with hook attachment, dissolve sugar in the warm water. Sprinkle in yeast and let stand until mixture is foamy, about 5 minutes.
Add 1 cup flour, olive oil and salt and stir with a wooden spoon. Slowly add remaining flour until a shaggy dough is formed. Knead for 10 minutes in the stand mixer until the dough comes together and is smooth.
Cover dough with a moist kitchen towel. Allow dough to rise in a warm, dark place, until the dough has doubled in size, about 1 hour.
Punch dough down and separate dough into 12 round pieces by pinching off some of the dough. Use your hands to tuck the sides and roll into an even ball, covering the pieces with a moist kitchen towel as you work. Allow to rest for 10 minutes.
Use a rolling pin to roll out the dough as evenly as possible. This is important to ensure that the pita puffs up. Transfer the rolled out pita onto small squares of parchment paper floured lightly.
Preheat oven 550°F (or to the highest temperature it will go) with the baking sheet inside the oven. While the oven is heating, allow the pita rounds to rest for about 30 minutes.
Flip the rolled out pita onto the heated baking sheet. Bake on the bottom rack of your oven until lightly golden brown and puffed, about 3-5 minutes. Wrap them in a clean kitchen towel as soon as they come out of the oven.
Notes
Storage: Store in an airtight container at room temperature for up to three days. Store in the fridge for up to five days.