Only by having the LLM random walk the hypothesis space with a validator rejecting invalid ones.
The reason why LLM hypotheses are any good is because it already consumed a civilization worth of knowledge. You couldn't have bootstrapped such system with nothing but a few priors/axioms and let it discover the universe.
Well yes, LLM need rich and favorable substrate to grow and learn (or we might say bootstrap)
As well as DNA needs specific substrate (cell with ribosomes and other machinery). As well as humans (one need oxygen atmosphere, food, parents).
But in the world we live in existence of favorable substrate for humans or LLMs is a given thing. It is _already_ bootstrapped. Can we infer something about LLM limits or possibility of it achieving AGI from its bootstrapping requirements?
Hrm I doubt it actually. Llms are capable of discovery, as recent math news showed. This means a "society" of Llms could likely have progress.