We have virtually no idea how consciousness arises in the human brain. Furthermore, what is “natural” supposed mean here, and why should it matter for consciousness whether some prerequisite arises naturally or not?

I think you have grazed my stance on this topic in the sense of what separates LLMs from complete human (or any other biological life) sentience.

It's the constant sensory input of the world and the realization and drive to survive as the second order effect of it. Mortality, vulnerability to external factors codified as input could in fact allow the LLM to independ as sentience.

Of course besides the sensors, it would also need a way to affect the physical world, and to be able to monitor the degradation if its own hardware, but when that barrier is crossed, it would be much closer to full sentience than whatever we have right now (which is nowhere near sentience or AGI).