In a small bowl, combine the warm water, yeast, and sugar. Let sit in a warm place for 15 minutes until yeast gets bubbly.
In a large mixer bowl, combine the gluten free flour, salt, 3/4 Cups of the olive oil, and the yeast mixture. Mix on low until blended. Remove from the mixture and knead on a lightly floured surface until everything is well blended. If the dough is too dry, add water 1 Tablespoon at a time until it becomes more moist and easier to knead.
Coat the inside of the mixing bowl with oil, place the dough in it, and cover with plastic wrap. Let sit in a warm place for 1 hour. You will not notice the rising as much as with traditional dough.
Pour 1/4 Cup olive oil onto a rimmed baking sheet and spread the dough over it to cover the sheet. Using your finger tips, push holes into the top of the dough, then brush the top with the remaining 1/4 C olive oil. Cover with plastic wrap and let sit another hour.
Preheat oven to 425 degrees F. Bake until the dough starts turning a light brown on top, about 15-20 minutes. Remove from oven and sprinkle with coarse salt and rosemary (for traditional focaccia) or top with the pizza toppings of your choice and return to the over for 5-7 minutes longer, until the cheese is melted and the toppings are heated through.