In a large mixing bowl, combine the warm water, sugar, and active dry yeast. Allow it to sit for about 5-10 minutes, or until it becomes frothy.
Once the yeast is frothy, add the flour, salt, and olive oil to the bowl. Mix with a wooden spoon or spatula until the ingredients are just combined. The dough will be sticky.
Transfer the dough to a floured surface and knead it for about 5-7 minutes, or until it becomes smooth and elastic. Sprinkle more flour if too sticky.
Form the dough into a ball and place it in a greased bowl. Cover it with plastic wrap or a clean kitchen towel and let it rise in a warm area for about 1-2 hours, or until doubled in size.
While the dough is rising, heat 1/4 cup olive oil in a small saucepan over low heat. Add smashed garlic and rosemary, infuse flavors for 5-10 minutes, then remove from heat.
After the first rise, punch down the dough to release air. Transfer to a greased baking sheet and stretch into a 1/2 inch thick rectangle or square. Create dimples all over the surface.
Cover the dough again and let it rise for another 30-45 minutes for an airy texture.
Preheat the oven to 425°F (220°C) while the dough is rising.
Brush the rosemary-garlic oil generously over the dough surface. Sprinkle with coarse salt. Bake for 20-25 minutes or until golden brown and fragrant.
Remove from oven and let cool on a wire rack. Slice into squares and serve warm.