In my OP, I did not mean specifically some LLM, but a hypothetical, scalable-past-human-capabilities synthetic brain.

Today it is a statistical model

I would argue that a human brain is a statistical model. Complex, but in the end it's a black box that takes in input from senses, and spits out output in form of interaction with environment. I'm not saying we and LLMs are in any way alike, or that AI is alive. But I do not agree with postulation that a true artificial thinking machine is impossible to build within next 1B years or however long Earth stays habitable for complex life.