The title of this question may have you puzzled. But, I'm combining ideas from this question about using a palapa ("tikki hut") and this question regarding using a hut built by a Gentile.
OK, let's say you find an existing palapa built by a Gentile. The roof is already there and the thatch is valid schach material. The palapa is open. Can you take a piece of canvas and create walls with a "doorway" and construct your succah that way? Or is there anything that requires that the walls must be built first?