Remove sourdough discard from fridge 30 minutes before starting, or use cold. Stir any separated liquid back in, then measure 1 cup (227g).
In a small bowl, combine warm water (110°F) and sugar. Sprinkle instant yeast over the surface and let stand for 5-10 minutes until foamy.
In a large mixing bowl or stand mixer bowl, combine the activated yeast mixture, sourdough discard, and olive oil. Stir briefly until combined.
Add bread flour and sea salt to the wet ingredients. Mix on low speed until incorporated, then increase to medium speed and knead for 7-10 minutes until smooth and elastic.
Shape dough into a smooth ball and place in a lightly oiled bowl. Turn to coat, cover with plastic wrap, and let rise at room temperature for 1 to 1.5 hours until doubled in size.
Place pizza stone or steel on middle rack and preheat oven to 500°F (260°C) for 45 minutes to 1 hour before baking.
Punch down dough, turn out onto a lightly floured surface, and divide into two equal portions for thin crust or leave as one for thick crust. Shape into balls and rest for 15 minutes.
Press or roll each dough ball into a disk, leaving a thicker border for the crust. Stretch to desired size and thickness.
Transfer shaped dough to a pizza peel dusted with semolina or directly to an oiled sheet pan. Add sauce, cheese, and toppings, keeping them light for best results.
Slide pizza onto preheated stone or steel (or place sheet pan in oven) and bake at 500°F (260°C) for 10-14 minutes for thin crust or 14-18 minutes for thick crust, until golden and bubbling.
Remove from oven, let rest for 2 minutes, then slice and serve hot.