A short article from inequality.org [1] suggests that most of the richest people in the world (Forbes 400) were born with significant financial advantages, if they weren't already wealthy.
Since there are many more rich people than the Forbes 400, that doesn't seem too representative of the usual rich person. It's hard to find anything conclusive - there are a few research memos put out by what seem to be wealth management firms claiming that most rich people are actually self-made. There's a clear conflict of interest here, so I'm not sure we can trust those results.
It seems understudied, and will take a lot more than 10 minutes of searching for relevant results.
1. https://inequality.org/research/selfmade-myth-hallucinating-...