> LLMs do it by ...

That they do it at all is the point and is what separates then from MP3 encoding algorithms. The "how" doesn't seem to me to be as important as you're suggesting.

You asked a hypothetical above about a different algorithm and now we've ascertained the reasons why that was reductive.

> LLMs never experienced ...

What is experience beyond taking input from the world around you and holding an understanding of it?

Toddlers learn over the course of several years of observing training data and for the first few years misspeak about themselves and others. What’s the difference?

How are you sure it doesn’t reason about itself? The grammar of languages encode the concepts of self and others. LLMs operate with those grammar structures and do so in increasingly accurate ways. Why would we say humans that exhibit the same behavior are inherently more likely to be conscious?