Combine warm water, sugar, and yeast; let foam 5–10 minutes.
Add gluten-free flour, almond flour, psyllium husk, baking powder, and salt to a mixer.
Slowly add yeast mixture and olive oil; mix on medium-high for 5 minutes.
Scrape bowl and mix again briefly.
Spread dough in pan with wet hands; cover and rise 45–60 minutes.
Heat oven with pizza stone at 425°F.
Press dough thinly into a 12-inch round; rise 10 minutes.
Bake crust alone 15–20 minutes.
Add toppings and slide onto pizza stone.
Cook 10–15 minutes until bubbling and crisp.
