In a large mixing bowl, combine the warm water, sugar, and active dry yeast. Stir gently and let it sit for 5-10 minutes until foamy, indicating the yeast is active.
Add 1/4 cup olive oil, salt, and 3 cups of the flour to the yeast mixture. Stir with a wooden spoon or your hands until a shaggy dough forms. Gradually add the remaining 1/4 cup flour as needed, kneading until the dough is soft and slightly sticky (about 5 minutes).
Transfer the dough to a lightly floured surface and knead for another 2-3 minutes until smooth. Place the dough in a lightly oiled bowl, cover with a damp towel, and let it rise in a warm place for 1 hour, or until doubled in size.
Preheat your oven to 425°F (220°C). Lightly oil a 9x13-inch baking sheet or pan. Punch down the risen dough and transfer it to the prepared pan. Press it out evenly with your fingers to fill the pan, creating dimples across the surface.
Drizzle 2 tablespoons of olive oil over the dough, then sprinkle with chopped rosemary, thyme, and coarse sea salt. If using optional toppings like Parmesan or olives, add them now. Let the dough rest for 15-20 minutes to puff up slightly.
Bake in the preheated oven for 20-25 minutes, until golden brown and crisp on the edges. Remove from the oven and let it cool slightly on a wire rack. Slice into squares or wedges and enjoy your olive oil and herb focaccia warm or at room temperature!