Sure, at the end it's a dice role, but you can get a better dice ;)

But your chances of being able to do that in the first place are massively dependent on your luck. It's a lot harder to get a degree or start a company if your family is struggling to afford essentials, or you're caring for a sick relative.

So for people who find themselves going into dept slavery, unable to feed themselves and their children well, unable to afford healthcare, and so on, you're saying it's all good, just a bad roll of the dice, nothing to worry about?

Seems to me more like the system is fundamentally broken if pure chance is all that seperates a millionaire and the destitute and downtrodden.

What assumption have you made about the system's purposes and functions? This is an important question and one we are currently wrestling with as a society. It's one of the BIG QUESTIONS and hard to answer. Plato's Republic might be a good starting place.

Social classes and social immobility are millenia-old phenomena and are completely independent of capitalism.