Background: I taught a short Introduction to Electronics to 1-2nd grade, Beginner Programming (Python) for 5-6th grade, and currently 3D Modeling and Printing for 5-6th grade. For better or worse I'm neither a qualified teacher not a qualified engineer, just a seasoned maker and a volunteer; and where I teach, the kids can choose whether to enroll to the class or not, so there's some "natural selection" to begin with.
My observations:
1. At least at such a young age, you can't really let them choose the projects they'd like to do, because (a) they lack the most basic practical knowledge, (b) they are not experienced in looking stuff up either, and (c) at this point they don't even really know their options, so they'll fall back on "robot" or "an app that [...]" or whatever the teacher hints. Even so, anything substantial they choose will be too much for them - unless you can team each and every kid with a mentor, to work on the specific skills required for his/her project. Instead, they can all learn a specific technique, and then practice it using "individual" projects which are variations on the theme.
2. Annoying and depressing as it may be, some kids simply have a natural talent for these things, and some don't*. This is not about previous exposure to STEM at home or otherwise, but about an appetite for riddles, logic, mechanics etc. In this sense (again, at the early ages I taught) I saw absolutely no difference between boys and girls.
* Of course, like any other trait, this talent for STEM is not really binary!
3. The natural talent is sometimes latent, and it appears and develops as the kid is exposed to new ideas, techniques, tools etc. So the very first thing to do, in order to get them into STEM, really is to expose them to it. They certainly aren't exposed to it in the media, or by playing with their smartphones. Most of them don't see it at home either. Again, this will definitely not make all of them into engineers, but it will help alleviate their fear of the unknown, and allow the talented ones to step forward and shine.
4. While it is impossible to advance without learning some theory, the worse thing to do is give them dry theory. I guess the same is true for most adults, too. The theory has to be incorporated into doing, into something they can see and/or touch. And this, unfortunately, is far more difficult than it sounds.