You are absolutely correct. Most millionaires in the US do not come from wealthy families. They earned their wealth, often through the kind of hard work that would make most snowflakes melt.
Some people are born into money, but it's only about 12% of millionaires that fall into that category.
For people attempting to attain wealth, the US is the greatest land of opportunity this planet has ever known, period.
https://www.businessnewsdaily.com/2871-how-most-millionaires-got-rich.html