Preheat oven to 450 degrees. Rub baking sheet with oil. Place tomatoes, garlic, and 1 tablespoon olive oil in a food processor; season with salt and pepper. Pulse 3 to 4 times until ingredients are incorporated but chunky.
On a lightly floured work surface, use a rolling pin and your hands to roll and stretch dough until large enough to cover the surface of the baking sheet. Transfer to prepared baking sheet.
Spread tomato sauce over dough, leaving a 1-inch border all around. Top with cheese and pine nuts; season with salt and pepper.
Bake until crust is golden, 15 to 20 minutes. Toss arugula with vinegar and 1 tablespoon oil; season with salt and pepper. Sprinkle arugula and olives over pizza.