The US actually lags behind most of western Europe and Canada in social mobility. Especially among the poorest.
"European Socialism" is not that different from the US. In Europe you may get free child care, health care, etc. and industries that the government likes get subsidies. In the US, this assistance comes in the form of tax cuts. Tax exemptions for employers who pay for health care, the child tax credit, tax deductions for favored industries, etc. Including tax expenditures, the US spends more on social welfare than most of western Europe while doing a poorer job of ensuring it reaches the right people.