Sure, a given LLM can only produce so much (though it might be a lot), and then you'll need fresh inputs. But you contend that those have to be human, while I am arguing that they could be

- random,

- from the environment,

- from other AIs.

That increases the space considerably.

In particular, note that your argument also applies to humans: A human, being finite, can only produce finitely many things. But you add other humans, the environment, and pure chance to the mix, and it'll be pretty infinite for all practical purposes.