Combine warm water, sugar, and yeast; let stand 5–10 minutes until foamy.
Combine gluten-free flour, almond flour, psyllium husk, baking powder, and salt.
Add yeast mixture and olive oil, then mix for 5 minutes until dough forms.
Cover and let rest 45–60 minutes until slightly puffy.
Press dough into a 12-inch round pan with oiled hands; let rest 10 minutes.
Bake crust without toppings for 15–20 minutes at 425°F.
Add toppings and bake another 10–15 minutes until golden and crisp.
Rest 5 minutes before slicing.
