not everyone who went to the Oz was a criminal -- tho plenty were.
there was a gold rush and for a while Melbourne was the largest city in the British Empire. plenty of actual "try my luck in the new world" folks landed, both in the 1800s and later.
During the founding wave the bulk of the poor were convicts.
During the founding of non convict colonies (Adelaide, Perth, etc) there was the mega rich of the day - second sons shipping out with entire households to establish footholds and means of trade, and their servants (by the terms of the day these were people with a position and a wage albeit not great).
The trying their luck in a gold rush etc crowd came after the founding of the main colonies, some convict, a number not.
FWiW in my estimation "Had a criminal record" | "was a convict" is distinct from "was a criminal" - the first two are a matter of record, the third is more of a judgement call of character.
Many sent to Australia as convicts had character, ethics, a trade, and were victims of circumstance, poor economics, the wrong politics, the wrong class, etc. rather than being of some essential criminal character.
there was a gold rush and for a while Melbourne was the largest city in the British Empire. plenty of actual "try my luck in the new world" folks landed, both in the 1800s and later.