Obviously we don't know what makes for consciousness, but it seems extremely likely that it requires some sort of persistent internal state and continuous experience. LLMs don't do either of those things after training.
Is our own experience really continuous? Or maybe we just perceive it as such?
Wouldn't the context window qualify as persistent internal state, and the expansion of the context be continuous experience? Even within the realm of computing a single token, I'm not sure what would separate the token generation process from the brain's own thinking process - the brain's experience, when looked at closely enough, is also not really "continuous" to a greater degree than procedurally moving from one state to the next.