Whisk together flour, water, and yeast in the bowl of an electric mixer. Cover bowl with plastic wrap, and let rise in a warm place until tripled in bulk and full of sponge-like bubbles, about 2 hours.
Add salt. Attach bowl to a mixer fitted with the dough hook. Mix on low speed 3 to 5 minutes, scraping down sides of bowl as needed. When dough begins to cling to and almost climb sides of bowl, raise speed to medium; mix 15 seconds. Dough will be wet, slack, and very sticky.
Using a plastic bowl scraper, turn out dough onto a well-floured work surface. (The dough will be hard to handle, but resist the urge to add flour to the top; instead, keep your hands and tools well floured.) With the bowl scraper (and, to a lesser degree, your fingertips), gather and fold bottom edge of dough about 1/3 of the way toward center. Pat down to deflate slightly and dislodge any extra flour. Fold top edge down 1/3 of the way toward center; the 2 folds should overlap slightly. Repeat with left and right sides, until all edges meet and overlap in center. Tap off excess flour as you work. Gently scoop up dough and flip it over, seam side down. Place dough in a lightly floured bowl, smooth side up. Cover bowl with plastic wrap, and let rise in a warm place until doubled in bulk, about 1 hour.
Return dough to a well-floured work surface. Repeat folding process, making sure to brush off excess flour. Lightly flour the mixing bowl, and return dough to bowl, smooth side up. Cover with plastic wrap, and let rise in a warm place until doubled in bulk again, about 1 hour.
Preheat oven to 450 degrees. with a rack in lower third. Coat a 17-by-12-inch rimmed baking sheet with 1/2 cup oil; set aside.
Place dough on prepared sheet. Flip dough over, and coat both sides with oil. Push dough out toward edges of sheet. Cover with plastic wrap; let rest 10 minutes. With plastic wrap still on top, press out dough to fill sheet. Remove plastic (dough should be very bubbly and supple). Drizzle remaining 1/4 cup oil over top. Sprinkle generously with sea salt.
Bake, rotating halfway through, until evenly browned on top and bottom, 25 to 30 minutes. Immediately slide focaccia onto a wire rack set over a rimmed baking sheet; pour any oil left in pan over top. Serve warm or at room temperature.