To me, I don't think the 'American Dream' means you are entitled to any set standard of life, nor that it is any kind of a guarantee that there is class equality. In it's purest terms I think it means that people still have the opportunity to make what they will of themselves and are able to be socially mobile without huge roadblocks standing in their way that make it impossible...it doesn't mean it's going to be easy, just achievable for those who work hard. And to that end I'd say the US is among the better places to live. Nobody tells you what job you 'will' have, being born in a barrio or a corn field doesn't mean that you are mandated to stay there for the rest of your life, anybody is free to go to college, and you can marry who you want regardless of race, as of recently even if you are both men/women. This doesn't mean people are 'guaranteed' to be successful or achieve a certain level of lifestyle/wealth, or that it's not much harder for some than others, just that they are available to families who reach out and grasp them.
My parents were born about as low as you can get on the 'social/economic ladder'. My father was 1 of 9 children on a farm in rural south dakota and was born in a 3 room cabin....he shared a room with his 5 brothers and was working on the farm since he could walk for their very poor family to even survive. My mother is an orphan from Vietnam who came to this country as a war refuge with literally just the clothes on her back and the extent of her English skills being limited to phrases from popular American songs playing there on the radio. Mostly by working incredibly hard, holding down jobs, not being proud and not considering things to be 'beneath them', not giving a crap what other people though, not paying others to do things they could do themselves, and being frugal, they were able to florish into a solidly middle class family. Not rich, not poor, but comfortable...and the middle class in America lives better than probably 80% of the world's population, so already I'd say that's achieving the dream for both of them that seemed far fetch from such humble origins.
In just one generation both of their children are extremely well educated, my sister is a physician and I have an MBA and work in business, with solidly upper middle class salaries....no, still not rich. But I married another person from a nice middle class family, no passed generational wealth to speak of, our jobs are decent but not fancy (my wife is a teacher)...and by the time my children are old enough to go to college their parents will have been millionaires for a decade.
All that progress in America within 2 generations. No huge 'breaks' were required, there's nothing overly special about our family. Just the willpower for my extremely poor parents to decide they wanted better, work hard for it, educate their children on how to work hard, and send them out in to the world with a little encouragement and the right skills, attitude, and approach to life to keep progressing higher.