Make the dough: Whisk the flour, sugar, salt and the yeast in a medium bowl. Pour the warm water into a large bowl, then add the flour mixture and stir until combined. Stir in 2 tablespoons olive oil to make a very sticky dough. Turn out onto a lightly floured surface and knead, dusting with more flour as needed, until the dough comes together and no longer sticks to your fingers, about 2 minutes. Transfer to a lightly oiled large bowl and turn to coat. Tightly cover with plastic wrap and refrigerate overnight.
Coat an 11-by-17-inch rimmed baking sheet with 3 tablespoons olive oil. Add the dough and stretch it to fit the baking sheet. Brush with the remaining 1 tablespoon olive oil. Loosely cover with plastic wrap and let rise at room temperature until puffy, about 2 hours.
Meanwhile, position a rack in the upper third of the oven and preheat to 450 degrees F. Make the sauce: Combine the tomatoes and their juices and the salt in a medium bowl and crush well with your hands or a potato masher. Uncover the dough and sprinkle with salt. Gently place the baking sheet in the oven (the dough might deflate if it is knocked). Bake until golden, about 20 minutes. Remove the crust from the oven, top with the sliced mozzarella and cover with 2 cups of the crushed tomatoes. Bake until the cheese is bubbling through the sauce and starts browning, 15 to 20 more minutes.
Let the pizza stand 10 minutes, then remove from the pan using a spatula and transfer to a cutting board. Let cool 1 to 2 minutes before slicing.