Australia became a British 'possession' on 28 April 1770

From the book of the title:

NEW SOUTH WALES - The Mother State, issued by the Intelligence Department, 1906.

Captain Cook, accompanied by Joseph Banks and Dr. Solander landed at Kurnell ... and took possession (i.e. no treaty or barter, therefore 'stolen' or under occupation) of the country in the name of King George III.

The book is available for download (478p, 59MB) at:
https://ia801404.us.archive.org/0/items/newsouthwalesmot00news/newsouthwalesmot00news.pdf