In a large bowl, mix the lukewarm water, yeast, and sugar. Let it sit for about 5 minutes until it starts to foam.
Add the flour and knead the dough for 10–15 minutes, until smooth and elastic.
Then add a good pinch of salt and about one-third of the olive oil.
Shape the dough into a ball, drizzle with a bit of olive oil to keep it from sticking, and place it back in the bowl. Cover and let it rise for 45–60 minutes, or until doubled in size.
Punch down the dough, transfer it to a lightly floured surface, and knead briefly by hand.
Shape it into a rectangle and place it on a greased baking sheet or in a baking pan. Cover again and let it rise for another 20–30 minutes.
Meanwhile, preheat your oven to 220°C / 425°F.
Brush the dough with another third of the olive oil and use your fingers to press deep dimples all over the surface: press firmly, almost touching the pan underneath.
Press halved cherry tomatoes and rosemary sprigs into some of the dimples.
Bake for 20–25 minutes, until golden brown. Once out of the oven, brush the focaccia with the remaining olive oil and sprinkle with salt to taste.