However, intellectual geniuses are better measured as people who revolutionized or significantly advanced the fields they worked in, and may have received recognition for doing so, not necessarily those who had highly visible worldwide impact, which is often more a matter of luck and different character attributes.
The people we recognize and celebrate as geniuses also tend to be people who had many accomplishments (because they were geniuses, not just one-time lucky), sometime seeing success on whatever they focused their attention on.
We wouldn't consider Tim Berners-Lee as a genius even though he certainly had world changing impact. Ditto for Demis Hassabis - certainly very smart, but hardly a Feymann. Someone like William Shockley also changed the world, and got plenty of recognition despite working for a commercial lab, but perhaps better regarded just as a bright engineer, right time right place.
AI is an interesting case, certainly changing the world, but the people who invented the tech, primarily Jacob Uszkoreit and Noam Shazeer, are really more akin to Berners-Lee and Shockley.
People like Von Neumann and Feymann, who shocked other geniuses with their intellect, really are a very rare breed. For people like this I'm not sure that "initial conditions" make much difference - they play by their own rules, and the world comes to them.