Activate the Yeast: In the bowl of a stand mixer fitted with a dough hook, combine the warm water and cane sugar. Sprinkle the active dry yeast over the mixture and stir gently. Let it sit for about 5 minutes until it becomes foamy. If the yeast doesn't foam, it's best to start over with fresh yeast.
Prepare the Dough: Add the all-purpose flour and sea salt to the yeast mixture. Mix on low speed until a shaggy dough forms. Increase the speed to medium and continue mixing for 5 minutes. The dough should be elastic, sticky, and begin to pull away from the sides of the bowl.
First Rise: Brush a large mixing bowl with 2 tablespoons of extra-virgin olive oil. Using a spatula, transfer the sticky dough into the oiled bowl. Lightly brush any excess oil from the edges over the surface of the dough. Cover the bowl with plastic wrap or a damp kitchen towel and let it rise in a warm place until it doubles in size, approximately 1 to 1½ hours.
Shape the Dough: Generously oil a 9x13-inch baking dish with another 2 tablespoons of olive oil. With oiled hands, gently deflate the risen dough by folding it into itself from the edges toward the center, forming a rough ball. Transfer this dough ball to the prepared baking dish, turning it to coat all sides in oil. Press the dough evenly to fit the dimensions of the pan. If it resists stretching, let it rest for a few minutes before trying again.
Second Rise: Cover the baking dish with plastic wrap or a damp towel and allow the dough to rise again until doubled in size, about 45 minutes. About 30 minutes into this rise, preheat your oven to 425°F (220°C).
Prepare for Baking: Once the dough has risen, drizzle the remaining 2 tablespoons of olive oil over the surface. With oiled fingers, press deep indentations (dimples) all over the dough, pressing down to the bottom of the pan without tearing the dough. Sprinkle with flaky sea salt and chopped fresh rosemary, if desired.
Bake: Place the baking dish in the preheated oven and bake for 20 to 30 minutes, or until the focaccia turns golden brown. Remove from the oven and let it cool slightly before serving.