Activating the yeast. Combine the yeast, sugar, and warm water. Mix gently in a large bowl and set aside until the mixture has combined and swelled to twice its original size, which should take about 15 minutes.
Preheating. Preheat the oven to 200 degrees F.
Combining the dry ingredients. Put the sorghum flour, brown rice flour, sweet rice flour, tapioca flour, potato starch, flaxseed meal, xanthan gum, baking soda, and salt into the bowl of your stand mixer. Turn on the mixer and combine the flours and other dry ingredients well.
Adding the liquids. Add the yeast mixture into the dry ingredients. Mix until just combined. Add the apple cider vinegar, then the eggs, one at a time, and then the olive oil. Allow the mixer to beat them into the dry ingredients, on low speed. Pour in the club soda in a slow drizzle. Pour in only as much as is needed to wet all the ingredients completely. The dough should feel soft and firm, like a baby's bottom.
Kneading the dough. Attach the dough hook to the mixer and stir the dough on medium speed for 5 minutes. This will give the dough a chance to cohere more evenly. It will also whip air into the dough, which will cut the usual density of gluten-free bread. After 5 minutes, turn off the mixer and transfer the dough to an oiled bowl. (If you do not have a stand mixer, knead the bread by hand on a gluten-free-floured surface, for at least 10 minutes.)
Allowing the dough to rise. Turn off the oven. Put the bowl into the oven, with a damp towel over the top of it. Leave the bowl in the oven for 90 minutes. The dough will not have risen much, at this point. There is no gluten to stimulate that rising. Accept that.
Baking the bread. After 1 hour, take the bowl out of the oven and put it on the stovetop to continue rising. Turn the oven on to 500 degrees F. Put a cast-iron pot, large enough to hold the bread, into the oven. (A cast-iron Dutch oven with an enamel surface is ideal, but any large pot or pan will do, as long as it has a lid.) Leave the Dutch oven in the oven for 30 minutes. Meanwhile, the dough will continue to rise on the stove.
After 30 minutes, carefully take the Dutch oven out of the oven. Without worrying too much about a perfect shape, transfer the wet dough into the hot Dutch oven. Put the lid on and immediately push the Dutch oven back into the hot oven. Do not turn down the heat. Allow the bread to cook for the entire 30 minutes. By the end, it will smell like freshly baked bread. Take the Dutch oven out of the oven, remove the lid, and voila -- a wonderfully crusted loaf of gluten-free bread. Allow the bread to cool for 10 minutes, then cut right into it.
Suggestions. For olive bread, add 1/2 cup of chopped kalamata olives into the dough. For rosemary bread, add 1 tablespoon of chopped fresh rosemary into the dough, then sprinkle thick crystals of sea salt on the top of the bread before baking. Be creative. At the end of the evening, slice up any remaining bread and put it into the freezer. Gluten-free bread usually turns rock hard the next day.