According to https://www.weforum.org/reports/global-social-mobility-index..., the US ranks 27th in social mobility, behind 21 European countries, and ahead of 14 of them.

On the "Education Access" pillar, the Netherlands scored highest, while the US ranks 40th. So I don't think your conclusion is accurate.

The US has significantly lower social mobility than most of Europe, though I think people kind of ignore that and pretend the opposite is true.

It's a lot easier to get in to college in the US than in most of Europe, but it costs a whole lot more (like requiring a degree in the first place, it's a kind of social gatekeeping). I think nowadays like 60% of high school grads attend some amount of college, but only about half of those get an actual degree.