In a small bowl, combine the warm water, sugar, and active dry yeast. Stir gently and let it sit for 5 to 10 minutes until the mixture becomes frothy.
In a large mixing bowl, whisk together the gluten-free flour, psyllium husk powder, baking powder, and salt until well combined.
Add the frothy yeast mixture, olive oil, and apple cider vinegar to the dry ingredients.
Mix the ingredients using a wooden spoon or a hand mixer with dough hooks until a dough forms. The dough should be slightly sticky but manageable. If too dry, add 1 to 2 tablespoons of warm water; if too wet, add a little more gluten-free flour.
Lightly grease a clean bowl with olive oil and place the dough inside. Cover the bowl with a clean kitchen towel or plastic wrap and let it rise in a warm place for 30 minutes.
Preheat your oven to 425°F (220°C). Line a baking sheet or pizza stone with parchment paper and lightly brush with olive oil.
Transfer the dough onto the prepared baking sheet. Using wet hands or a rolling pin between two sheets of parchment paper, shape the dough into a 12-inch round pizza crust about 1/4 inch thick.
Bake the crust in the preheated oven for 12 minutes until it starts to set but is not fully browned.
Remove the crust from the oven, add your desired toppings, and return to the oven to bake for an additional 8 minutes or until the crust is golden and toppings are cooked.
Remove the pizza from the oven, let it cool for 5 minutes, slice, and serve.