It doesn’t take any of that to grow existing wealth. You just invest it. You pay someone to do it, but honestly even just an ETF does the trick.
The U.S. is fairly exceptional in the fact that it is isolated from the world's woe. This stability is what helps you grow.
So it's true that some families that were wealthy 500 years ago are still wealthy today, but this was not the norm.
You would need to get a record of who was wealthy 300 years ago, track down their descendents, and see who among those descendants is "wealthy" by some measure today.
You might also need to take into account things like inheritance and birthrights. I imagine first born sons of first born sons might preserve more of the wealth.
Also, what proportion of the rich today are "new rich", and how newly rich are they?
It's not unusual by any means. There was a study on, I think, Genoese families that showed that wealth had more or less stayed within the same families for 300 years.