According to Hofstede's cultural dimensions theory, the USA and Australia have very similar cultures, although 'mateship' is not a dimension considered I will admit. :D
https://en.wikipedia.org/wiki/Hofstede%27s_cultural_dimensio... https://www.hofstede-insights.com/country-comparison/austral...
I would suggest that all national cultures value loyal friendship and working as a team. That said, 'mateship' has a sense of egalitarianism to it, and while Australia and the USA are egalitarian cultures, that is lacking in other nations, e.g., China.
https://www.hofstede-insights.com/country-comparison/austral...