Whisk flour, sugar, and yeast together in a large bowl. Add water and 2 tablespoons oil and stir until no dry flour remains, about 1 minute. Cover and let sit for 20 minutes.
Sprinkle table salt over dough and mix with your wet hand until salt is fully incorporated. With your wet hand, grasp edge of dough, stretch upward, and fold toward opposite side of bowl. Turn bowl 90 degrees and stretch and fold again. Continue to turn, stretch, and fold until dough is slightly tighter and smoother, about 30 times, re-wetting your hand if dough sticks. Cover and let sit for 20 minutes.
Lightly spray bottom and sides of a 13x9 inch baking pan with vegetable spray. Place 16x12 inch sheet of parchment paper over pan and, using both hands, press parchment down and into corners. Smooth parchment so it is flush with pan bottom and sides. Spread 3 tablespoons oil over bottom of pan.
Lightly dampen counter and your hands with water. Transfer dough to counter and gently press and stretch into 15x10 inch rectangle - dough will be sticky. Fold in thirds like business letter to create 10 x5 inch rectangle - use bench scraper if necessary to release dough from counter. Invert dough into prepared pan. Swirl to coat with oil, turn over and press to expel large air pockets. Cover and let sit until dough is puffy and jiggly and has flowed toward corners of pan, 2½-3 hours
About 20 minutes bfeofre dough has finished resting, adjust oven rack to middle position and heat oven to 475°
Drizzle remaining 1 tablespoon of oil over top of dough. Dimple dough all over with your wet fingertips, pressing all the way to the bottom of pan, pushing dough into corners, and breaking up any bubbles larger than 1 inch. Sprinkle with flake salt. Bake until deeply browned, 16-20 minutes, rotating pan halfway through baking.
Using spatula, transfer focaccia to wire rack. Let cool for at least 20 minutes before serving.
