There were plenty of CSA regiments with full uniforms. It was mostly organized per company, though, and the standard CSA uniforms that the government quickly made were pretty much ignored by the men alltogether. Men brought a shitload of stuff from home, especially things like waistcoats, but the southern states issued plenty of stuff. They even had their own uniform rules, sometimes. Of course, the reality was quite a bit different from the theory, but I really wouldn't say 0% of the CSA was uniformed at the start of the war. I think the percentage was pretty standard until the mid-war, after which it started to drop.