Combine the warm water, sugar, and instant yeast in a large mixing bowl. Stir gently and let sit for about 5 minutes until frothy.
Add the all-purpose flour, salt, minced garlic, and half of the chopped rosemary and thyme to the yeast mixture. Pour in the olive oil and mix until a shaggy dough forms.
Transfer the dough to a lightly floured surface and knead for 8 to 10 minutes until smooth, elastic, and slightly tacky. Add flour if too sticky, but sparingly.
Lightly oil a large bowl; place the dough inside and turn to coat with oil. Cover and let rise in a warm spot for 1 to 1.5 hours until doubled in size.
Grease a 9x13-inch baking pan generously with olive oil.
Punch down the risen dough and transfer to the prepared pan. Stretch evenly and create dimples all over with your fingertips.
Sprinkle remaining rosemary and thyme on top. Press halved cherry tomatoes and sliced black olives gently into the dough. Drizzle olive oil and sprinkle coarse sea salt.
Let the dough rest and rise for another 30 minutes to become light and fluffy.
Preheat oven to 425°F (220°C). Bake focaccia for 20 to 25 minutes until golden brown and edges are crisp.
Remove from oven and cool slightly before slicing. Serve warm or at room temperature with olive oil or dips.