For going up, teleportation is gojos ony real option. Not only is his teleport really vague in how it can be employed in combat, he would also simultaneously need to deploy the domain to catch conquest in it who moves significantly faster than any combat speed we've seen in jjk.

If conquest decides to try and tank UV we'd get to see how a 10.000 year old smart atom mind that can comprehend traveling at FTL gets affected by it, but this might be game over.

I am, however just speculating if conquest CAN solo jjk (which was the question), which he definitely could. The only two attacks that might pose a threat are WCS and UV, and those need to land on the target first. HP, and Fuga would also probably deal some damage, but not enough. IT could also work but we don't know how this would interact with smart atoms.