A head start is a moat iff you can't move easily from the leader to a competitor that catches up qualitatively; nvidia’s headstart against AMD is a moat to the extent that you can't just take the software written against NVidia GPUs and run it on AMD if AMD catches up. (That is, being currently ahead isn't a moat, but it can impose switching costs which are.)
Taking code that runs against one hosted LLM and running it against a different backend LLM is... not generally a big deal. So OpenAI being ahead—in the core model, at least—is just being ahead, its not a moat.