If this is a class-ridden society denying "access" to upward mobility to those at the bottom, why is it that immigrants can come here at the bottom and then rise to the top?
This is a
non sequitur. Many immigrants who "rise to the top" are well-educated: more so than many Americans.
Also, many immigrants who appear to 'rise to the top' were in fact from the top of their own societies, and brought capital with them or had access to the borrowing of capital from other upper-class family members. Of course as Emsworth pointed out above the educational level of successful immigrants is typically very high - another indication they came from the upper class in their own countries.