Even if you don't have your own tomato sauce, you can still make this from-scratch pizza. Use fresh tomatoes or canned San Marzano tomatoes.
Preheat oven to 450 degrees. If using a pizza stone, place on bottom rack. Combine yeast with the water; let stand about 5 minutes until creamy. Combine flour and salt in a food processor. Add yeast mixture and 4 1/2 teaspoons olive oil; process just until dough comes together. Turn out onto a lightly floured surface. Knead 1 minute; shape into a ball. Place in a lightly oiled bowl; turn to coat, and cover with plastic wrap. Leave in a warm place until dough has doubled in bulk, about 1 hour.
Pulse tomatoes in the bowl of a food processor fitted with the metal blade until largest pieces are about 1/2 inch. Gently punch down dough; divide into two pieces. Sprinkle a pizza peel or inverted baking sheet with polenta or cornmeal. Stretch one piece of dough on surface to an 11-inch round; rub with 1 tablespoon olive oil. Spread half the tomatoes on top, leaving a 1/2-inch border all around.
Slide onto pizza stone, or place baking sheet in oven. Bake 10 minutes; sprinkle half the cheese on top. Bake 5 minutes more, or until crust is crisp and cheese is melted. Remove from oven; sprinkle with half the oregano and red pepper, if using. Repeat with remaining ingredients. Serve hot.