In the large bowl, combine the warm water, active dry yeast, and the sugar. Over the next few minutes allow the yeast to become active.
In a large bowl add the sourdough starter, flour, salt, and active yeast. Mix until a sticky dough forms. Cover the bowl with plastic wrap or a homemade bowl cover and allow the dough to rest for 15 minutes. After the initial rest, use wet hands to perform 3 sets of stretch and folds, spaced 15 minutes apart. To do this, gently grab one side of the dough, lift it up to stretch slightly, and fold it over toward the center. Rotate the bowl a quarter turn and repeat the process from each side until you've done it four times total—this counts as one set. Let the dough rest for 15 minutes, then repeat the stretch and fold process two more times. This simple technique helps build gluten strength and structure without kneading, resulting in a soft, airy focaccia with a beautiful rise.
After the final stretch and fold, cover the bowl and let the dough perform its first rise at room temperature for about 30 minutes to 45 minutes, or until doubled.
Once the dough has doubled in size, pour 3 tablespoons (40 g) of olive oil in a 9x13-inch rectangular pan (or a cake pan) lined with parchment paper. Make sure the oil is evenly dispersed. Transfer the dough to the prepared pan and gently stretch it to fit. Cover with plastic wrap (or a damp kitchen towel or homemade bowl cover) and allow it to do a second rise at room temperature for 45–60 minutes, or until it has doubled in size once again.
Preheat oven to 425°F. With oiled fingers, dimple the top of the dough all over. Drizzle with the remaining 3 tablespoons of olive oil, and sprinkle with the fresh rosemary and coarse sea salt, or your favorite toppings.
Place the baking pan in a preheated oven and bake for about 25 minutes or until golden brown and crisp on top. Let cool completely before slicing. Enjoy!