The only times i had succes with yasuo as carry was in earth elemental games.
Ideally you get yasuo with a belt or recurve right from the start, or another unit holding that item and find yasuo in the early rounds.
Now all he has to do is stack up some nice HP and you slap some titanic hydra onto him, ideally 2hydras and later into the game(after raprtors, or if you're healthy enough, even later) you want to move him off the elemental field and add a warmongs.
Though there are other options, Hurricane synergieses well with hydra, and getting PD if you struggle vs crit users or Iceborn/FH for some overall tankiness do work aswell if you can't find enough belts. Spear also is a 3ed item option to get those ults going.
The main issue of yasuo is that he either doesn't do that much damage, or he dies to quickly. With the mountain hp stacking, he usually gets beefy enough, and with titanic+bladmaster and his ult, he still does the needed damage.
Obviously you want him to reach lvl 3, so you can't really aim for lvl 9, if you don't have a good start you might even have to choose between lvl 8 and a somewhat realistic chance of 3 stars.
The only other built i can imagin is with either cloud quiana or cloud lux, giveing him IE, BT and Quicksilver. That's certainly enough damage, some sustain, the much needed CC immunity, 50 mr, which together with the mystik bonus(usually you automatically get that with janna+yi) is quite alot mr, and +40% dodge so he theoretically should not die to easily.
If you already have quiana, you might try yomuus instead of IE, though unless yout get to lvl 9, fitting 6 assasins into the comp is rather difficult and the assasin 3 bonus is MUCH weaker that IE.
But usually he works better as supportive champ, either left alone, doing some damage and haveing a nice CC onto a priority target while you ivnest your resources elsewhere, or you give him tank gear. Iceborn is great cause of the synergie with the cloud dodge, warmongs can be good unless to much opponents have GW, Swordbreaker and hush are great, he basically perma CCs an priority target useing those with his ult.
Though frankly, sivir is a better user as she can apply them multiple targets, so in a blademaster comp you usually give them to her.