In a spacious mixing bowl, combine the warm water and instant yeast. Stir gently, then allow it to sit for about 5 minutes until it becomes frothy, indicating the yeast is activated.
To the yeast mixture, add the flour, salt, and ¼ cup of olive oil. Mix together until a shaggy dough forms.
Transfer the dough to a lightly floured work surface. Knead the dough for approximately 5-7 minutes, or until it turns smooth and elastic.
Grease a large bowl with a little olive oil and place the kneaded dough inside. Cover the bowl with a damp cloth or plastic wrap, and let it rise in a warm environment for about 1 hour, or until the dough has doubled in size.
After the dough has risen, gently punch it down to release any air bubbles. Turn it out onto a greased baking sheet or a large, rimmed baking pan.
Carefully stretch and press the dough until it fills the pan evenly. Use your fingertips to create dimples all over the surface, making sure they are deep enough to hold oil and toppings.
Drizzle additional olive oil over the surface, and then sprinkle the chopped rosemary and coarse sea salt evenly. If using, press halved cherry tomatoes into some of the dimples, enhancing both flavor and presentation.
Allow the dough to rest for another 30 minutes while you preheat your oven to 425°F (220°C).
Bake the focaccia in the preheated oven for 20-25 minutes, watching for it to turn golden brown and develop a crisp exterior.
Once baked, remove the focaccia from the oven and allow it to cool slightly on a wire rack before slicing into squares.
Notes
Serve warm, optionally drizzle with olive oil or balsamic reduction.