Preheat your oven to 400°F (200°C).
In a large mixing bowl, whisk together the all-purpose flour, baking powder, and salt until well combined.
Add the plain Greek yogurt and 1/4 cup olive oil to the dry ingredients.
Using a wooden spoon or your hands, mix until a soft dough forms. If the dough is too sticky, add a little more flour, one tablespoon at a time.
Lightly flour a clean surface and turn the dough out onto it. Knead gently for about 1 minute until smooth.
Transfer the dough to a baking sheet lined with parchment paper.
Using your fingers, gently press and stretch the dough into a roughly 9×12 inch rectangle, about 1/2 inch thick.
Drizzle a little olive oil over the top of the dough.
Sprinkle the garlic powder, chopped fresh rosemary, and coarse sea salt evenly over the dough.
Using your fingers, create dimples all over the surface of the dough by pressing down gently.
Bake in the preheated oven for 20-25 minutes, or until the focaccia is golden brown and cooked through.
Remove from the oven and let cool slightly before slicing and serving.