Gödel’s incompleteness says almost nothing about this. I wish people wouldn’t try to apply it in ways that it very clearly is not applicable to.
An environment living in Conway’s Game of Life could be quite capable of hypothesizing that it is implemented in Conway’s Game of Life.
Now the question is are we in Conways Game of Life?
Indeed, as I think I commented before here, this kind of self-reference is exactly what makes Gödel's proof work.