I'm sorry but this is factually incorrect and I'm not sure what experts you are referring to here about there being concensus on this topic. I would love know. Geoffrey Hinton, Demis Hassabis, and Yann LeCun all heavily disagree with what you claim.

I think you might be confusing creation ex nihilo with combinatorial synthesis which LLMs excel at. The proposed scenario is a fantastic testcase for exactly this. This doesn't cover verification of course but that's not the question here. The question is wether an already known valid postulate can be synthesized.