A British colony in founded 1788 and all of its implications for the existing Indigenous population was, when they set off, intended for Botany Bay, precisely because that was the most important stop of Cook's expedition and members of Cook's expedition recommended it to the British as the location of where they should form a new colony largely due to the aftermath of losing the American colonies due to the American Revolution. One linked to the other. In terms of creating a British colony, Cook was clearly the most important single figure.
Going by some of the posts in this thread, people would have been fine if it Captain Cook was replaced with Governor Phillip, who was both head of the First Fleet expedition and the first Governer, because "Cook was just an explorer and had nothing to do with colonisiation", which is silly, because Phillip didn't make the decision to colonise, he was just attached to it as part of his job, unlike Cook's expedition. If you're going to name someone as the starting point, from an indigenous POV as to the colonisation process, of course it's clearly Cook. Without his expedition the British wouldn't have known that there was a Botany Bay in the first place to try to colonise (until they realised that Port Jackskon was a better harbour at the end of their trip just a bit north).
I hope the above wasn't political and is just a general retelling of Australian history, that, you know, I have read up on in the past because if I'm going to try to comment and understand the context of things like Welcome to Country (rather than just ignore or whatever and get on with my life, which is fine too), that it's my obligation to try and understand the context of history.
The starting point goes back a lot further than Cook.