But language is also the only way to communicate this. As far as I can tell my cat has a complex consciousnesses but there is no way for me to tell if she has this capacity for introspection and self-reflexivity.

If there are other avenues other than language, how would we know?

I think language is a medium that enables this kind of structured thought. Without it, I cannot imagine reaching this level of abstraction (understanding being a "self").