Anecdotally, it feels true. I, like many Americans, know an enormous number of immigrants and poor people that moved into the middle and upper-middle class through hard work and discipline. There is still plenty of opportunity to do that US if you apply yourself. Economic mobility is very high in the US (which is distinct from social mobility).
When I've worked in Europe, it has always been evident that this is much harder to achieve there for poor people and immigrants. The entire social system is setup to limit the ability of ambitious people to rise above whatever station they were born into in a way that isn't really a thing in the US. This contributes to why engineering wages are relatively low in Europe.
The US ranks very high in terms of absolute mobility. Measures of relative mobility are only comparable between countries if they have similar wage compression curves, which is also partially a function of country size. US wages are much less compressed than in Europe -- see also: engineering wages -- so they aren't meaningfully comparable in relative terms.
Given two countries with the same median wage (PPP), a 20k increase in income in one country may be relatively "economically mobile" and a 40k increase in income in the other is not, even though the income increase is much larger in real terms. When average people talk about economic mobility, they mean the second case; using relative mobility is misleading.
When I've worked in Europe, it has always been evident that this is much harder to achieve there for poor people and immigrants. The entire social system is setup to limit the ability of ambitious people to rise above whatever station they were born into in a way that isn't really a thing in the US. This contributes to why engineering wages are relatively low in Europe.