You have further to go to actually make it into the upper classes than in many countries.
Educational achievement is uneven and often runs in families. Single mother dropped out of school? Odds are greatly in favor of your dropping out of school. Few high-school dropouts in the upper classes. Blame it on uneven economic development, micro-cultural attitudes, whatever.
Class mobility is defined as being born and raised in one class and moving into another. So if you start with nothing but your upbringing and stay in that class it's assumed that somehow you actually took stuff--money, property, etc. Often the case in European countries. Not so much the case here.
I'm pretty much the same class as my parents. The only property I actually got from them was a car (high school graduation present) and $3000, which was actually the cashing out of my life insurance policy when I turned 18 and which I kept until last year (I'm in my 50s now).
In fact, it was also the case with my parents and their parents. Yet my parents parents left precisely nothing to my parents. At 18 my father left home; at 17, my mother. My mother--a single mother in the '50s--got some help from her mother, a roof over her head. But when she left home again she took her own income, her child, and her clothes.
It was the same with my wife before we got married--and with her parents, who only inherited a small amount when they were in their 50s.
The last two generations in my family started off with pretty much nothing when they left home. They weren't upwardly mobile, because their lifestyle in their teen years, which took them a decade or more to recreate, was very much like their final adult lifestyle. This isn't "upwardly mobile," by the operant definition.