In fact I’d bet a lot more people think to themselves that they are only successful because they are a genius than there are geniuses. Because it’s even more likely that coming from a highly rich or well connected family is truly the key factor in their success, and people would would much rather attribute success to talent or intelligence than daddy.
It is definitely true though that prodigious talent isn’t by itself sufficient to be successful. Also, intelligence helping you is kind of a given - it’d be like an NBA player saying “being 6’8” really helps”. There are a lot of really tall people not in the NBA and a lot of prodigiously talented people who aren’t conventionally “successful” either.
Where does one get intelligence from? Your intelligence is inherited from your parents (just like any other physical characteristic), so if your biological parents have an extensive influence on your upbringing, it's completely possible that both nature and nurture, almost your entire existence, all your qualities, can be reasonably attributed to the family into which you were born.
I don't think many people asked Yao Ming if being 7'6" helped with his basketball career, or Michael Phelps if his human flipper feet helped win a medal or two. But they have spoken at length about how they trained for their careers, and sane people can understand that being a genetic freak doesn't make you a world class anything. It predisposes you to success if you seek it - and both those people spent an enormous amount of their youth working to get there.
The point is that success is not determined before you're born, and reasonable people understand that there's such a thing as variance in human anatomy.
Success financially (depending on what threshold you use) is largely ruled out by birth for most everyone ever born. Exceptions occur, and some places and time periods may have afforded the opportunity to more people, yet always a sliver.
So technically success isn't entirely determined before you're born. But for most it is at least off the table, unless the threshold is very low or they are exceptionally lucky and driven.
For top .0001% success in some fields (most sports, for example), you need genetic qualities AND hard work.