Remove sourdough discard from refrigerator 1 hour before making dough. Stir to smooth out and ensure it's at 100% hydration.
In a large mixing bowl, combine warm water and sugar. Sprinkle instant yeast over top, stir, and let sit for 5 minutes until foamy.
Add sourdough discard, olive oil, and salt to the yeast mixture and stir well until incorporated.
Add 2 cups of flour and stir until a shaggy dough forms. Continue adding flour in 1/4 cup increments until dough forms a ball and pulls away from the bowl sides.
Knead dough on a lightly floured surface for 8-10 minutes by hand, or use a stand mixer with dough hook for 6-8 minutes, until smooth and elastic.
Place dough in a lightly greased bowl, cover with plastic wrap or a damp towel, and let rise at room temperature for 1-1.5 hours until doubled in size.
Gently press down dough to release gas. Turn out onto floured surface and divide into 8 equal pieces (90-100g each). Roll each piece into a ball and rest for 10-15 minutes.
Roll each dough ball on a lightly floured surface into a 6-7 inch circle about 1/8 inch thick.
Heat a dry cast iron skillet over medium-high heat for 5 minutes. Place one pita disk in the skillet and cook for 1.5-2 minutes until bubbles form and it begins to puff. Flip and cook 1-1.5 minutes more.
Remove pita from pan and immediately wrap in a towel or place in a towel-lined basket to keep soft. Repeat with remaining dough.