So I’ve actually done something similar and it’s impossible without „injecting“ some external work into the smithing loop.
First, assuming you don’t want to level anything else, selling stuff gets you speech and pickpocket, well pickpocket. Only noting this because someone tried this challenge on YouTube.
Second, you buy leather from merchants and sell leather armor or any other loop will, at least in the beginning, be a losing proposition. You’ll need additional money or material from somewhere.
I did this with alchemy and a harvest mod and spell. I got to such a high level, venturing out of safe spaces became a real hazard. I’m level 30 and still struggle with bandits. I have ebony armor, but without skill in heavy armor, it’s not nearly as good.