If you’re looking for proof you’re begging the question, asking for a formal proof of something that by definition can’t be proven, which only makes sense if your philosophical basis is that reality is a formal system. Other people have other philosophical bases, and while they may not be formally probable, they can be supported with other evidence that is equally strong, pointing to the non determinism of quantum physics or the infinitely recursive question of “what caused the first cause”.

The strongest evidence I have is that people are notoriously difficult to predict, individually.

Do pattern matching engines get out of bed in the morning and make breakfast?

Humans can ask questions and seek out information. LLMs can only respond to questions.