Spot on guidance. In the Navy engineering majors (see exact list if desired) are Tier 1 majors while professional flight students are Tier 2.
One detail as food for additional thought though - those commissioning into the Armed Forces can't 100% guarantee that they'll be trained to fly by the military even if they commission and serve. Some very interested in flying people with Aeronautics/ UAS/ Aero Eng. graduates end up on sub, swo nuc, cyber, NFOs, etc. service assignments - it's ultimately based on the needs of the ____ (Navy, Army, Air Force). Every year including this fall, we saw a lot of heartbreak from posters here and IRL who wanted to fly, and will not be.
So, we all only get so many journeys around the sun, and if you or your young adult is 100% certain that in this lifetime they NEED to be a pilot and to serve, even if you aren't provided the opportunity to fly for the military while you serve as an officer, then the hedge bet here is to get your commercial license and a big chunk of your restricted R-ATP qual hours before commissioning and serving with professional flight - becoming a pilot as a college major. In that path, you when you get out will have less hours (R-ATP at present is 1000 hours) and in short order will get scooped up by the airlines and on your way.
The path of being approx 27, with an eng. degree, five years experience as a swo or whatever officer, then working toward your ATP with1500 hours for years when at that point you may have a family to support and you're working for 20-25 hours per week as a CFI - eventually - isn't great. The cost too until you get your commercial can be very high. Don't get me wrong, Eng degrees are highly marketable for $$$ positions - no need to cry in one's soup for them, but - I'm just speaking to those candidates for whom flying as a career in this lifetime is a must-do to consider this option. It's not cheap, but getting the training is a great way to secure your future in the skies . *and if you are a female candidate, lots of scholarships to cover flight fees (which ROTC does not cover) because of the shortage of STEM women in this field.
Anyone interested in learning more about this option is welcome to DM me.