In the bowl of a stand mixer fitted with the paddle attachment, stir together flour, Platinum Instant Sourdough Yeast, and kosher salt by hand. Add warm water and 2 tablespoons (28g) oil; beat at medium speed for 5 minutes.
Lightly oil a large bowl. Place dough in bowl, turning to grease top. Cover and let rise in a warm, draft-free place (75°F/24°C) until doubled in size, 45 minutes to 1 hour.
Grease a rimmed half-sheet baking pan with 2 tablespoons (28g) oil. Turn out dough onto prepared baking sheet. With oiled fingers, gently press dough into a 10-inch circle. Loosely cover with plastic wrap, and let rest in a warm, draft-free place (75°F/24°C) for 30 minutes.
With oiled fingers, press dough into a 14x11-inch oval. Loosely cover with plastic wrap, and let rise in a warm, draft-free place (75°F/24°C) until puffed, 25 to 30 minutes.
Preheat oven to 425°F (220°C).
Gently press dimples into surface of dough. Drizzle with remaining 1 tablespoon (14g) oil. Top with tomatoes, rosemary, and garlic. Sprinkle with sea salt.
Bake until golden brown, 15 to 20 minutes. Let cool on pan for 10 minutes. Serve warm or at room temperature.