Grease your pizza stone or baking pan and lightly sprinkle gluten-free cornmeal or rice flour over it. This will help prevent the pizza from sticking to the surface. Preheat the oven to 425 F. If you use cornmeal, check that it is actually gluten-free. Some commercial brands add wheat flour to cornmeal.
In a large bowl, mix together tapioca starch, sorghum flour, chickpea flour, brown rice flour, xanthan gum, salt, and sugar. If brown rice flours give baked goods a grittier taste than you prefer, substitute with white rice flour.
Next, proof the yeast to make sure it is actually still active. Add the packet to a cup of warm water. In about 10 to 15 minutes, the yeast should bubble and look creamy. If this happens, add the yeast and water to the dry ingredients along with the oil, eggs, and vinegar. If this doesn't happen, repeat the proofing with a new packet of yeast.
Beat the dough with an electric mixer until thick, smooth, and sticky. The consistency of the mixture will be between that of bread dough and batter.
Remove the dough from the bowl and lightly flatten it with wet hands to create a thin shell. Since there is no gluten, you need to be gentler than you would with regular pizza dough. Make sure you keep your hands wet throughout the process to prevent the dough from sticking to your skin. Let the crust rise for about 15 minutes before placing it in the oven.
Bake for about 10 minutes in the oven until golden. Remove your crust from the oven and add your sauce and toppings. Return the pizza to the oven for another 10 to 15 minutes.