In a small bowl, combine the warm water, yeast, and sugar. Stir gently and let it sit for 5-10 minutes until foamy.
In a large mixing bowl, whisk together the gluten free all-purpose flour, potato starch, tapioca starch, salt, and baking powder until well combined.
In a separate medium bowl, whisk together the melted butter, eggs, apple cider vinegar, and Greek yogurt until smooth.
Pour the wet ingredients into the dry ingredients and mix with a sturdy spoon or stand mixer fitted with a paddle attachment on medium speed until fully combined.
Add the activated yeast mixture to the dough and mix for an additional 2 minutes to incorporate and activate the yeast.
Transfer the dough into a greased 9×5-inch loaf pan and smooth the top with a wet spatula or your fingers.
Cover the loaf pan loosely with a clean kitchen towel and let the dough rise in a warm, draft-free place for 45 minutes to 1 hour, or until the dough has risen to about 1 inch above the rim of the pan.
Preheat the oven to 375°F (190°C) while the dough is rising.
Once risen, bake the bread in the preheated oven for 45-50 minutes, or until the top is golden brown and a toothpick inserted in the center comes out clean.
Remove the bread from the oven and let it cool in the pan for 10 minutes.
Transfer the bread to a wire rack and cool completely before slicing to prevent crumbling.