1) Define "ties with money."
2) Even if there was someone in the family that had money that doesn't mean the person benefited. I don't know any relatives 3 steps out, but I do know that both of my parents were entirely self-made. If there was someone farther out with money it couldn't have any bearing.
So, your parents were "made". You have available wealth immediately. Not even a single step.
And "entirely self made" is bullshit. I know my own family history and I see what made their legacy, and they wouldn't have been allowed to make themselves had they been black. They never would have gotten their feet in the door for a loan and you know as well as I that such momentum carries more now than ever.
Wealth here defined as "has a home with a spare room, and a mortgage, and no real fear of losing it, even with a vagrant family member on the couch".