Who do you consider rich?
My spouse and I became successful by living on less than we earned, all our adult lives. Even working low-wage jobs, we were able to add to our savings accounts. We invested our money in long-term-growth stocks and continued to be fairly frugal.
My parents died first. I inherited $20,000, enough to pay off our mortgage. Without house payments to make, we were able to save a whole lot more. We paid for our cars, our next house, our kids' college, up-front. By the time we inherited after the death of my spouse's parents, while we were happy to have the money, we didn't need it.
My parents' main contribution was in teaching us both to handle money and credit responsibly. Unlike a lot of people I know, we've never been unable to pay our credit cards in full, afford an unexpected repair that's necessary, or delayed getting medical treatment because of money.