It was literally his mission to find land to steal and place the natives under British rule

Actually, it ends up looking even worse for Cook. His instructions specifically said:

You are also with the Consent of the Natives to take Possession of Convenient Situations in the Country in the Name of the King of Great Britain: Or: if you find the Country uninhabited take Possession for his Majesty by setting up Proper Marks and Inscriptions, as first discoverers and possessors.

So either he ignored the Crown’s instructions to get “consent”, or he (and not later colonists) is the original source of claims of terra nullius.