In the bowl of a stand mixer fitted with a dough hook, stir together 1¾ cups warm water and 2 teaspoons cane sugar. Sprinkle 1 (¼-ounce) package active dry yeast (2¼ teaspoons) on top and stir again. Set aside for 5 minutes, or until the yeast is foamy. If the yeast doesn’t foam, discard and start again with new yeast.
Add 500 grams (4 cups) all-purpose flour and 2 teaspoons sea salt to the yeast mixture. Mix on low speed until a shaggy dough forms. Increase the speed to medium and mix for 5 minutes. The dough should be very elastic and sticky, starting to grab the sides of the bowl.
Brush a large bowl with 2 tablespoons of olive oil. Using a spatula, transfer the sticky dough from the mixer bowl to the oiled bowl. Lightly brush any oil pooling at the edges over the surface of the dough. Cover the bowl with plastic wrap or a damp towel and set aside until the dough has doubled in size, 1 to 1½ hours.
Brush a 9x13-inch baking dish with another 2 tablespoons of olive oil. Uncover the dough and rub your hands with olive oil. Slide your hand under one edge of the dough and fold it into itself, working your way around the bowl until you have a rough ball.
Transfer the dough to the prepared pan and turn to coat in the oil. Gently press the dough to the pan’s edges. If it pulls away, let it rest for a few minutes, then press again until it reaches the edges.
Cover the pan with plastic wrap or a damp towel and let the dough rise until doubled in size, about 45 minutes.(30 minutes into this rise, preheat your oven to 425°F.)
Remove the cover. Drizzle the remaining 2 tablespoons olive oil over the dough. Rub your hands with olive oil, then use your fingers to make deep indentations all over the surface. Sprinkle with flaky sea salt and chopped fresh rosemary, if desired.
Bake in the preheated oven for 20 to 30 minutes, or until golden brown.
Let the focaccia cool in the pan for a few minutes, then transfer to a wire rack. Serve warm or at room temperature.