One of my patients was a project manager at JPL and a professor at Caltech. He told me straight up that “it doesn’t matter where your son goes to school.” He went on to say what mattered was curiosity and drive and that some of his most pedestrian engineers were from Caltech.
Look into where the NASA site directors went to undergrad, all state schools, most of them random, with one single exception, RPI. No MIT, CMU, Caltech, etc.
Don’t overthink this.