American culture is not a monolith. This can vary greatly in different regions or different subcultures.
On average, Australian culture views anyone, who even passively demonstrates any significant level of achievement, with a high degree of suspicion. Australians make a national sport of cutting down people who excel in any way. Sure, there are sub-cultures there which can vary considerably from this general trend, but even they feel the influence of this prevailing attitude. The end outcome is that Australians tend to go to considerable effort to hide the things that may single them out as excelling among their peers, and emphasise those things which make them similar. (A few months ago the CEO of the most powerful retail company in Australia gave an interview attempting to reduce public ire at their price gouging tactics, dressed in the uniform of a shelf stacker from their supermarket chain. I'm not saying this could not have happened in America, but there it would have probably been seen as a stunt or a statement... in Australia dressing any other way would have raised eyebrows, and in fact most people initially failed to even notice it for the PR manipulation that it was.)
Geographic proximity will always play a role in bringing cultural norms together, and while the US is a big place, the US population throughout the 20th century had incredible mobility, going where the jobs were, which helped to tighten up that bell curve.
In the US if you have wealth it's plausible that you had a great idea that got acquired, or a great skill.
What's lacking is a general habit of boasting about this, being wealthy, letting others in the country (ie. yourself) know about it.
You can find first generation pretty wealthy Australians in trucking, factory ownership, real estate, mining, warehouse volume sales, etc. Of those the ones most likely to be flash about their cash would be the real estate crowd, success in house sales is hard to come by without prominent self promotion.
Real estate wealth is a bit prominent, bit doesn't really have the same tone as designing or building something, more a reflection of our current dirt obsession.
But almost every wealthy American tells a story about how they did it by themselves, ignoring the schools that they attended, the services which were available to them, the people their parents associated with, and the ability to make high-risk investments because they had a built-in security net.
How to reconcile? It's fairly easy ... there aren't that many millionaires. The US has a society, culture and economy that allows for their occurence perhaps "better" than most other places. But this doesn't reflect the likely economic pathway that most of the population experiences in life.
America is good at generating millionaires (which ain't what it used to be)! News at 11!
I find the obsession we have with saying we have a problem with success absolutely does not translate to my lived experience here. I see it on the national stage where the moment someone fucks up everyone piles on, but usually they’ve been on a path to being a flog for a long time anyway and they need, at the very least, a reality check.
Think how much better Elon musk’s headspace could be if one person in his circle had told him ‘you are mortal’ regularly along his journey of multiple triumphs
Pretty much everything else you said confirms just how ingrained the attitude under discussion is in this country. Which is hardly surprising. If it was perceived as aberrant by the majority then it wouldn't be commonplace.