[qqtt]

Just to put a button this excellent summary, the classic example of "rearranging words to form a sentence that we think has meaning" that Wittgenstein uses in Investigations is the question: "What is the meaning of life?"

We think intuitively that because we constructed this sentence with words, that it must have meaning, and must have an answer - as you say, it is flipping the causal relationship between starting with a sign and using language versus starting with language and trying to find a sign. This question is ultimately the latter.