Instead of cotton we could wear animal skins... but that would require killing lots of animals. Or we could wear polyester which is made from petroleum... or we could take all issues of “Tree Hugger” magazine - I assume the print version is made from trees - and glue them to our bodies to keep warm.
You can take chicken feathers and turn it into fibers of either silk like softness or wool like warmth they all are the same animal protein polymer. Dissolve the proteins in a organic solvent push that through a spinner and Bob’s your uncle. Why chicken feathers because there is millions of lbs a year of it going to landfills or being put in the ground as compost.
Another choice is use cellulose from whatever source you choose the list is legion being the most common biological polymer on the planet. From the forests to the oceans cellulose is what holds plants together. Dissolve that in acetone,or a similar polar solvent then again push that through a spinner nozzle at pressure making fiber of what ever thickness you desire from silk to cotton. Cellulose to fiber has a commercial name rayon it’s over 50 years old. Humans will never be short of fiber it’s how cheap do you want it. Scientists have been GMO blue green algae to grow in salt water and excrete cellulose and sucrose directly to the growth medium. Blue green algae are the most efficient converters of sunlight to mass of any organism ten times that of land plants while using brackish or salt water nothing else could grow in. Remember cows eat cellulose as their primary energy source and monogastrics eat sucrose a six carbon sugar as our primary energy source. Having a ten times increase per square meter of land area is no small feat.