In a small bowl, combine warm water, sugar, and yeast. Let it sit for about 5-10 minutes until bubbly and foamy.
In a large mixing bowl, combine the flour and salt. Make a well in the center and pour in the yeasty mixture along with 1/4 cup of olive oil.
Mix with a wooden spoon until a soft dough forms.
Knead the dough on a floured surface for about 8-10 minutes until it becomes smooth and elastic.
Place the dough in a lightly greased bowl, cover it with a damp cloth, and let it rise in a warm place for about 1-2 hours, or until it doubles in size.
Preheat your oven to 400°F (200°C) while the dough is rising.
Once risen, punch down the dough and turn it out onto a greased baking sheet or a stone. Stretch and shape it into a rectangle about 1 inch thick.
Using your fingers, create deep dimples all over the surface of the dough.
In a small bowl, mix the minced garlic with the chopped rosemary and a drizzle of olive oil. Brush this mixture generously over the dough.
Sprinkle coarse sea salt over the top and let it rise for another 20-30 minutes.
Bake in the preheated oven for 20-25 minutes, or until golden brown.
Remove from the oven and let it cool slightly before cutting into pieces.