My mother often talked about children she'd witnessed talking about their past lives. She believed it but I'm sceptical. Then my son started saying things like "when I was a girl" which seemed to confirm it and my mother thought so until I told her he also talked about "when I was James the red Engine" and it became clear this was him recounting stories from books but in the first person. He quickly grew out of it as…
I just had this talk with someone else's mother, and didn't know how to carry the conversation. Going along with what-if was my best option.
However, your hypothesis is very compelling.
Context about developing self-awareness (from some random site): https://www.fatherly.com/health/children-five-stages-self-aw...