In a large bowl, using a wooden spoon or dough whisk, stir together the flour, salt, sugar, and yeast. Pour in the warm water and 2 tablespoons of olive oil. Continue mixing until no more dry flour appears in the bottom of the bowl.
Dust a clean work surface with flour. Transfer the dough to your floured work surface and knead it until it comes together in a smooth ball that is tacky but doesn't stick to your hands. This should take about 5 minutes. To knead the dough, place the heel of your hand (or both hands) on the center of the dough and press down and away from you. Fold the dough up and over, turn the dough 45 degrees to the right, and repeat, sprinkling with a little flour as needed if the dough keeps sticking to your hands.
Drizzle 1 tablespoon of olive oil into a large bowl (preferably one with a tight-fitting lid). Place the dough ball in the bowl and turn to coat it in the oil. Cover the bowl with a lid or plastic wrap and let the dough rise until it doubles in volume, 1 to 2 hours at room temperature or overnight in the refrigerator. (If refrigerating the dough, take it out of the fridge about an hour before you proceed to the next step so it can come back to room temperature.)
Grease a large (13 x 18-inch) rimmed baking sheet with 2 to 3 tablespoons of olive oil. Place the dough in the pan and press it out with your fingers until it reaches all the way to the edges and corners of the pan. If the dough keeps shrinking back, let it rest for 10 to 15 minutes and try again. After the dough is pressed out all the way to the edges of the pan, cover the whole pan with plastic wrap or a clean kitchen towel and let it rest (proof) for 30 minutes or up to 2 hours. (The longer the dough proofs, the more it will puff up and the fluffier your finished pizza crust will be. For grandma-style pizza, 30 minutes is all you need. For traditional Sicilian-style pizza, 1 to 2 hours is best.).
Preheat the oven to 500°F. Top the dough with sauce, cheese, and any other meats and veggies you like.
Transfer the baking sheet to the oven. Bake the pizza for 15 minutes, rotating the pan once halfway through, until the bottom of the crust is golden brown. (Use a spatula to carefully lift up one corner of the pizza to check underneath.)
Remove the pizza from the oven. Let it cool for 5 minutes, then cut into squares and serve.