In a small bowl, combine the warm water, sugar, and yeast. Stir gently and let it sit for 8 to 10 minutes until foamy.
In a large bowl, whisk together the gluten free flour, tapioca starch, psyllium husk powder, and salt.
Add the egg whites, olive oil, and apple cider vinegar to the yeast mixture and whisk until combined. Pour into the dry ingredients and stir vigorously for 2 to 3 minutes until a smooth, sticky dough forms.
Line a baking sheet with parchment paper and lightly dust with gluten free flour. Divide the dough in half. With well-oiled hands, shape each piece into a long log about 12 to 14 inches long and place them on the prepared sheet, spaced a few inches apart.
Smooth the surface with damp fingers. Cover loosely with greased plastic wrap and let rise in a warm spot for 40 to 50 minutes, until noticeably puffed. Preheat the oven to 425 F and place an oven-safe dish on the bottom rack. Score the tops of the baguettes with 3 to 4 shallow diagonal slashes. Pour half a cup of hot water into the dish on the bottom rack to create steam, and immediately place the baguettes in the oven.
Bake for 22 to 28 minutes, until the crust is golden brown and crisp and the internal temperature reaches 205 F.
Let the baguettes cool on a wire rack for at least 20 minutes before slicing. The crust will be beautifully crisp, and the interior soft and airy.