"The American Dream" isn't very old. Here is a Google Ngram chart that shows the history of the expression
in print:
See? 1930, the beginning of the worst crisis in capitalism and writers started talking about this American Dream.
Unfortunately I do not have a chart that reveals whether the American Dream has succeeded, failed, or never existed in the first place. We do have history, however, and it is clear that capitalism was developed in England and was exported to the colonies. I can't say whether it was the British Empire or the United States that most fulfilled capitalism's potential. Let's call it a draw. And let's not forget Europe, South America, Asia, and Africa. Capitalism is alive and well all over, for good or for ill.
Capitalism = "The American Dream"? Maybe? Probably? Obviously? I don't know.
The American Dream was bought with credit. It was bought with resources borrowed (or taken) from ecosystems, non-renewable energy, indigenous peoples, etc., not just money borrowed from banks. This borrowing was wreckless. A lot of consumption more than investing. Externalities not included in the prices of that consumption. — WISDOMfromPO-MO
I think you will find that this is a pattern which is far older than the United States. There is no way for any organism to exist without using resources from ecosystems. As for the rest, sure: non-renewable energy, seizure of indigenous resources through genocide, reckless, costs externalized, etc. All true.
Capitalism is not sustainable--anywhere. To the extent that capitalism = the American Dream, then neither is sustainable.
This next comments will seem like they are totally off-topic, but it actually are not:
I've been reading the Doomsday Machine by Daniel Ellsberg. Ellsberg worked for the RAND Corporation in the 1950s and '60s as a national defense analyst and strategist. He became well acquainted with American nuclear war strategies at the time. He was appalled to discover that the US had a first-strike strategy; Command and Control was sloppy at best; authority to launch nuclear weapons was delegated by Eisenhower and subsequently followed by several presidents; the plan was all out attack on both the Soviet Union and China -- regardless of whether China was involved in whatever threat the USSR was thought to pose. The plan called for the destruction of every significant city in the USSR and China.
Kennedy wanted to know what the human cost would be -- assuming that all of our bombs reached their targets and no weapons were launched from the USSR. The military had a ready answer: around 700 million in Europe and Asia. The military planners, however, had not included deaths from fire storms, which they should have because they knew all about firestorms from Hamburg, Dresden, Tokyo, Hiroshima, and Nagasaki. A quite reasonable estimation of total deaths would be closer to 1 billion -- then 1/3 of the world's population.
The assumption was that the USA would survive the fallout from this massive attack with little or no cost. At the time, the concept of nuclear winter had not been developed. Ellsberg notes that the US still has enough missiles (about 400) and nuclear-armed submarines to bring about nuclear winter, even if we were the only ones to fire off our atomic weapons--because of the fire storms boosting massive tonnage of soot into the high atmosphere where it would remain for years--blocking a lot of sunlight and chilling the planet significantly -- causing a massive kill off of many species, including humans.
One might hope that America and the American military are not one and the same thing. At the very least, the ideas of Manifest Destiny and American Exceptionalism are ticking away in their heads, and in the heads of a lot of civilians too.