You’ve clearly misunderstood, and don’t know what the null hypothesis is. In scientific philosophy, (that is, the philosophical foundation of science, not philosophy that uses science) “overcoming the null hypothesis” or “rejecting the null hypothesis” means you have enough evidence to say that you know something. Furthermore, there is a difference between saying “I don’t believe that is the case” and saying “I believe that is not the case.” One is a declaration of ignorance, and the other is declaration of certainty. They could infact not be more different from an epistemic standpoint. Also, for the purposes of this discussion, whether I believe humans have self-awareness isn’t actually relevant; we are discussing the justification for believing that animals have self-awareness. Furthermore, there’s no such thing as a “default state” and being part of the same clade or other constructed set as a sophont strikes me as a generally utterly irrelevant factor in determining whether an entity is itself self-aware baring some evidence that there is a relation conveyed by being in that set that itself indicates self-awareness.

TLDR: your argument is bad, and you should educate yourself in philosophy. Particularly epistemology and logic.