In a small bowl, combine the warm water, sugar, and active dry yeast. Stir gently and let sit for 5 to 10 minutes until the mixture is foamy.
In a large mixing bowl, whisk together the flour and fine sea salt.
Make a well in the center of the flour mixture and pour in the yeast mixture and 1/4 cup olive oil.
Using a wooden spoon or your hands, mix until a rough dough forms.
Turn the dough onto a lightly floured surface and knead for about 8 to 10 minutes until smooth and elastic. Alternatively, use a stand mixer fitted with a dough hook and knead on medium speed for 6 to 7 minutes.
Lightly oil a large bowl with olive oil. Place the dough in the bowl and turn to coat it with oil. Cover the bowl with a clean kitchen towel or plastic wrap.
Let the dough rise in a warm, draft-free place for about 1 hour or until doubled in size.
Generously oil a 9×13-inch (23×33 cm) baking pan with olive oil.
Punch down the risen dough and transfer it to the prepared pan. Gently stretch and press the dough out to fill the pan evenly.
Cover the dough loosely with a kitchen towel and let it rise again for 20 to 30 minutes until puffy.
Preheat your oven to 425°F (220°C).
Using your fingertips, dimple the surface of the dough all over, pressing down about 1/2 inch deep.
Drizzle 2 tablespoons of olive oil evenly over the dough.
Sprinkle the chopped rosemary and coarse sea salt over the top.
Bake the focaccia in the preheated oven for 20 to 25 minutes until golden brown and cooked through.
Remove from the oven and let cool in the pan for 5 minutes.
Transfer the focaccia to a wire rack to cool slightly before slicing and serving.