I wonder if there's some social constraints that babies naturally seem to rebel against (or at least be less interested in). Cooks used to be mostly women, now they're mostly men. Accountants used to be mostly men, now they're mostly women. https://www.weforum.org/agenda/2016/03/a-visual-history-of-g...
Programming is a good example here. It used to be women's work, mainly because it was relegated to women (men didn't want to do it, and it was seen as not that important). Now it's reversed; there's lots of money in it.
This is frequently repeated but rarely with supporting data. Programming work during the 70s and 80s, during which women's representation in programming reached its peak, was well paid. According to the BLS entry level salaries were $20k for the lowest level of "computer programmer" and $40k for the highest. Entry level "systems analyst" is listed with $28k salary [1]. The current BLS statistics for computer programmers does not break down by seniority, but lists an average annual income of $90k [2]. Adjusted for inflation, and the salaries are pretty similar. In Silicon Valley, entry level salaries above $100k are common but this is not replicated nation wide.
Pink was once for boys.
On the other hand it seems that infant chimps and rhesus monkeys play with gendered toys - https://www.theguardian.com/science/2010/dec/20/chimps-play-...
It seems like nurture isn't naturally all that strong except in certain circumstances.