In a small bowl, combine the warm water, sugar, and active dry yeast. Stir gently and let it sit for 5-10 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 dry ingredients and pour in the yeast mixture and 1/4 cup olive oil.
Using a wooden spoon or your hands, mix until a sticky dough forms.
Turn the dough onto a lightly floured surface and knead for about 8-10 minutes until smooth and elastic. Add a little flour if the dough is too sticky, but keep it soft.
Lightly oil a large bowl with olive oil and place the dough inside, turning it to coat all sides 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 it has doubled in size.
Preheat your oven to 425°F (220°C).
Lightly oil a 9×13 inch (23×33 cm) baking pan.
Punch down the dough to release air and transfer it to the prepared baking pan. Press the dough out evenly to fill the pan.
Using your fingertips, gently dimple the surface of the dough all over.
Drizzle 2 tablespoons of olive oil evenly over the top of the dough.
Sprinkle the chopped rosemary and coarse sea salt evenly over the surface.
Let the dough rest for 15 minutes to rise slightly again.
Bake in the preheated oven for 20-25 minutes, or until the focaccia is golden brown and cooked through.
Remove from the oven and let cool slightly in the pan before slicing and serving.