A Microsoft researcher built a goat-powered LLM in Age of Empires II to prove it's not sentient
(www.xda-developers.com)
There may not be proof that LLMs aren't sentient, but there is some evidence and reason to believe that consciousness is an emergent property of quantum effects, whereas turing machines are relegated to classical mechanics. The same evidence would indicate it is unlikely that a turing machine could replicate the human brain since it uses fundamentally different layers of reality to calculate/think.