Don't we? Maybe someone with more architectural knowledge of LLM systems can fill in the gaps in my knowledge, but where's the feedback loop that would allow actual self-awareness to develop? FAFAIK, LLM's are feed-forward networks. There are neither small cycles spanning a few nodes, nor integral cycles allowing the model to see what it's outputting -- the only feedback it gets is through the training process, which does not act as a mirror.
I struggle to see how self-awareness would ever manifest from a system that cannot experience its own output.