> Is it even possible that a complete simulation of the rules of this universe (let alone the content of it) could exist in this universe?

Yes, it is possible! See how a Quine is constructed.

https://en.wikipedia.org/wiki/Quine_(computing)

As an analogy: you can have a zip archive that expands to itself. Or even more so: to itself (the simulation of itself in itself) plus something arbitrary (standing in for the rest of the universe).