Really?
Every rich person I know started rich.
They had a house/flat bought, fully paid, and fully furnished when starting uni. Not necessarily a grandiose one, but one, nevertheless. So already, light years ahead of most others in terms of saving, investments etc.
They had their education fully paid for so no debt.
They had good contacts, so started immediately with good internships, and very good starter jobs.
They had various inheritances at various stages - grand parents, parents, bachelor uncle etc. Most of those went back into investments/ property etc.
Most had parents who started saving for their children's (the parents grandchildren) education as soon as they were born, so the wealth stays generational, the cycle continues.
And ALL really respect money. I see very few of them in a high turnover designer clothes, cars etc. In spite of very well to do circumstances, I see frugality, not too much extravagance, and well thought out indulgences.
They live well, but don't flash the cash.
OP - you are correct. Some people break through, but most are on a cycle.