More generally I’d argue that the American dream is that we made a country with greater social mobility than any other. That from any start, through hard work and intelligence you could become either middle class or rich according to your will. That the only thing holding you back would be your ability to capitalize on opportunities.
It is of course, a dream that was either never true or has ended. It is demonstrably false that the US has greater social mobility than many of our contemporary first world countries. While there is still opportunity here, and social mobility is far from impossible, the rich get richer and the poor stay poor is probably closer to the truth of modern America than the American dream of a fully socially mobile society.