AGI is definitely possible - there is nothing fundamentally different in the human brain that would surpass a Turing machine's computational power (unless you believe in some higher powers, etc).

We are just meat-computers.

But at the same time, there is absolutely no indication or reason to believe that this wave of AI hype is the AGI one and that LLMs can be scaled further. We absolutely don't know almost anything about the nature of human intelligence, so we can't even really claim whether we are close or far.