I have four adult daughters... and a Chinese wife. One of my daughters in a med tech, the next is getting her Doctorate of Nurse Anesthesia Practice, the next is in her final year of medical school, and the youngest has a degree in business information systems: data analytics with a minor in math. My wife started her how successful property services company 9 years ago.
Why did I say "Chinese" wife? Because Chinese culture is heavily focused on education with an emphasis on STEM education. I kid my children were "doomed" to be STEM majors.
My youngest daughter's roommates were all engineering or nursing majors (two went into mechanical engineering and the other one into computer engineering), the fifth graduated with a BS in Nursing. They were not Chinese, but at least one of their parents was an engineer, except the Nurse. Her mother was a nurse.
My daughters loved Disney Princess movies, played with dolls, enjoyed reading fashion magazines, and all the other "girly stuff" people attribute to young girls. One was a musician, one loved clay pottery, one was an athlete, and one loved choir.
Where am I going with this? Simply I do not buy that "girl play" undermines young girl's becoming STEM majors and there is no reason to discourage girls doing those things.
However, I do think there are several things a family can do to impact their children's careers. First, expose them to STEM. My youngest daughter was in a math tutoring program that many Asian students do called Kumon. Of the four girls she loves computers and programming, while the other daughters see them as tools. My oldest three daughters were exposed to health care by virtue of my career in health care and each gravitated to it.
Another thing, we exposed our daughters through movies with women in leaderships roles. Everything from League of their Own to Hidden Figures. Seeing examples of women individually and collectively excelling in science and sports based on real life stories can be inspiring.
There is nothing wrong with other majors and fields of study. But I do believe STEM offers both boys and girls and better chance of earning a good income provided they have the aptitude for a career in that field. As parents we can promote interest in them (or if your wife is Chinese, relentlessly push STEM). But in the end, nothing is worse than a career you hate.
