Did Britain invade or discover Australia?
Humans first discovered Australia about 40,000 years ago and like everything else about your question, that's debatable!
The UK were not the first to discover Australia, but they were the last to discover it, so I guess that means they "discovered" Australia.
The UK did not ‘Invade' Australia, they invaded it. Small ‘i'. A very important distinction. There was no military invasion in that sense of the word, but like a weed invades a field, they did invade. And from the indigenous population that died defending their land and way of life the UK did Invade. From the UK's perspective and representatives, there was no opposition and no ‘war', the place was called ‘Terra Nullius' or ‘No-mans land'. The largest military unit deployed to put-down (kill) some ungrateful indigenous people was a company (about 100 men).
So the answer to your question is both yes and no. It all about perspective.
Point of interest: The Brits only bothered to colonise Aus. because of their rising prison populations becoming untenable, Transportation to the other colonies no longer being available their having rebelled. Yes, the brand new the USA. (Always makes me smile when my Australian wife gets teased by Yanks about her convict heritage, same as theirs!) When the Brits landed at a lovely circular bay to start the penal colony, they named it after the Home Secretary who had ordered it, Lord Sydney, and made it a Hell on Earth. Now its the best city in the world, I know, I live here! (Government still sucks though!)
There are two distinct questions here...
Firstly, the British did not " discover " Australia...there was a large Aboriginal population already living there when the first Europeans arrived...therefore Britain could not have discovered Australia. When you throw in South East Asian contact and other European explorers ( Dutch )...the Brits were late to the party.
As Ernest W. Adams points out, Captain Cook did not " invade " Australia...however, Captain Arthur Phillip did....as Commander of the First Fleet and the first Governor of the new colony in 1788, he arrived with a technologically superior ( if not numerically ) force and took possession of a whole continent for the English crown....he was just the first of many to come.
There was NO treaty with the existing inhabitants.
There was NO bill of sale...no negotiations..they just came and took what they wanted and the Aboriginals could go to hell if they didn't like it.
Did these people come halfway across the world with the express orders to " invade " this new land....no, of course not...but that was the real world effect of their arrival on the Aboriginal inhabitants...their land was taken from them and they were killed if they got in the way....sounds like an invasion to me.
Britain did not discover Australia in the sense of being the first people to find it, obviously. Southeast Asians had found it centuries before. There had been reports by Western explorers of a large southern continent whose full extent was unknown. It was first known to Europeans as New Holland, having been spotted by the Dutch. But the British explored it far more extensively. Captain Cook also determined that New Zealand was a collection of islands and not part of Australia (early reports were uncertain).
Captain Cook did not "invade" Australia, contrary to certain revisionist claims. His sealed orders required him to enter into friendly relations with the natives, to begin trade with them, and to take possession of useful regions of land with their consent.
Later British visitors were far less scrupulous, and obviously colonized the place at sword point. However, the term invasion has a specific meaning that shouldn't be muddled up.
I guess no Britain did not discover Australia in a literal sense
"The European exploration of Australia was the exploration of Australia by Europeans, encompassing several waves of seafarers and land explorers. The first documented encounter was that of Dutch navigator Willem Janszoon, in 1606. The most famous of the explorers was that of Royal Navy Lieutenant (later Captain) James Cook 164 years later, who after an assignment to make observations of the 1769 Venus Transit, followed Admiralty instructions to explore the south Pacific for the reported Terra Australis and on 19 April 1770 sighted the south-eastern coast of Australia and became the first recorded European to explore the eastern coastline. Explorers by land and sea continued to survey the continent for some years after settlement."
Regarding invasion. Clearly the opposing side of an conflict have a very different perception.
I have difficulty equating the mostly hired ships of the First Fleet loaded with miserable convicts and their warders as an invasion fleet. And the later waves of free settlers - really people taking a huge risk to escape grinding poverty in Europe. Really one can draw a parallel with the current waves of economic migrants seeking a better life (in Europe of Australasia). If the British settlers were classed as invaders rather than economic refugees, I guess the term should also be applied to all economic refugees.
No, rather I would classify the early settlers as squatters - rather than invaders. And the absence of any treaty as an advantage since there were non to break, as would surely have happened (as in the US) under the relentless pressure of individual settlers seeking a better life.
"Did Britain invade or discover Australia?"
The British did not discover Australia in any sense at all.
By the time James Cook was sent to map the eastern coast of the continent Dutch and other navigators over the preceding 160 years had mapped the coast from the western side of Cape York all the way around the west and south to St Vincents Gulf, as well as part of Tasmania.
Cook was sent to map the remaining coastline of a known continent.
Discovery of the continent long predated that. It had been discovered by its earliest immigrants more than 40,000 years ago, then by Proto-Dravidian people around 6000 years ago, then again by Buginese ("Makassar") traders around 800 years ago. It may even have been discovered by the Chinese in the Twelfth Century as well as by several other groups of people throughout the tens of thousands of years from first known settlement.
Only the most servile of British Empire apologists would see James Cook as having "discovered" Australia. Cook was an outstanding navigator but he was not the discoverer of Australia.
However the British clearly did invade Australia. Largely not by their army as such, although there was some of that. For the most part it was by paramilitary forces including police and troopers, and by ordinary British subjects licensed by the government to seize for grazing the lands of the people already resident. The government also chose not to notice the murders and massacres of indigenous people, whether by weapons, poisons or deliberately-propagated diseases.
There might be discussions about who actually "discovered" Australia and there might be discussions on the meanings of "invade" verb - is it valid when European country attacks hunter-gatherers tribes. I prefer "colonize" word for what British Empire did to Australia.