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 all-purpose 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.
Transfer the dough to a lightly floured surface and knead for about 8 to 10 minutes until smooth and elastic. Alternatively, knead with a stand mixer fitted with a dough hook for 6 to 7 minutes.
Lightly oil a large bowl with olive oil. Place the dough in the bowl and turn it to coat with oil.
Cover the bowl with a clean kitchen towel or plastic wrap and let the dough rise in a warm place for about 1 hour, or until doubled in size.
Generously oil a 9×13 inch (23×33 cm) baking pan.
Punch down the risen dough and transfer it to the prepared pan. Use your fingers to gently stretch and press the dough evenly to the edges of the pan.
Cover the dough with a towel and let it rise again for 20 to 30 minutes until puffy.
Preheat the oven to 425°F (220°C).
Using your fingertips, dimple the surface of the dough all over, pressing about 1/2 inch deep.
Drizzle 2 tablespoons of olive oil evenly over the dough.
Sprinkle the chopped fresh rosemary and coarse sea salt evenly on top.
Bake the focaccia in the preheated oven for 20 to 25 minutes, or until the top is golden brown and the bread sounds hollow when tapped.
Remove from the oven and let cool in the pan for 5 minutes.
Transfer to a wire rack to cool slightly before slicing and serving.