I had a theory that the basic Australian 'Pumas' were mostly introduced golden cats from Indonesia, perhaps of an unusually large size. Golden cats are a poorly-understood group and there are cryptid candidate golden cats for both the African and South Asian cats, which are medium-sized puma-like cats. Heuvelmans thinks the Mngwa is an unusually coloured giant variety of the African golden cat and I might submit some photo ref. for that idea some time.
In this case, there is some genetic evidence for cats that were introduced into Australia from Indonesia at 6000 years ago approximately: one of my professors at IUPUI mentioned that he had done research that demonstrated that.
(Incidentally, I have heard some good definitive reports of jaguarundis running loose in both Illinois and Indiana, but that is also another matter for another time)
However, in the case of the Australian cats, something else is happening that is very unusual: some of the leopard-sized cats are being killed and then tested, and their DNA turns out to be ordinary house-cat-derived.
It is thought that these Maine coon cats are related to the equally large and thick-furred Scandinavian skogskat, also known as the viking cat. I have done up a comparison for the big cat as compared to a more average one: actually the reports have them getting even bigger than I have shown, but showing the large size as big as reported makes it look too unreasonable.
And it also seems that rumour has it that Americans allowed pet or mascot pumas to run loose in Australia, allegedly both in the late 1800s and in WWII. I would not be surprised if that was also the reason for 'Panther' reports in New Zealand, Fiji and Hawaii.