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?
The Rama (OC 635) rules that at least 1 Tefach (height) of the walls must precede the Sekhakh. Otherwise it would invalid because of "Taaseh veLo Min heAsui" (having the item come into being, not being made directly) like the case of digging in a haystack (Sukkah 16a).