This is fairly obvious. Live in a household where education is valued, go to a school with good education, surround yourself with kids who also value education. Of course your likelihood for earning better than average will go up. If you grow up in a household where education is not valued, then you will most likely not be able to succeed as easily. Is this somehow controversial?
My parents grew up poor in a war-torn country. They left the country as soon as they could. However, they concentrated on education, and left on scholarships. My family lived a very middle class life but much better than anything my parents lived in. They had the exact same focus on education for me and my siblings. They sacrificed everything for our education. I went to a public school but I studied harder and worked harder than most of my friends, and I'm now a single-digit millionaire, which isn't very much in Silicon Valley but good enough for me. I'm currently retired at this point while I take care of my kids and my wife works because she wants to. My children will get the same focus on education and hard work, the way I did. My family went from poor to rich in a single generation.
Our cleaner is an illegal immigrant from Central America. Her daughter was born in the US and is going to a very prestigious private high school in the Bay Area and has plans of going to Yale. I know she will do it. They are also going from poor to rich in a single generation.
Generational mobility from poor to rich is easily possible, but you can only do it through hard work and education.