Could I apply to an elite university as a junior in high school? (ie skip senior year)

Fwiw, I didn’t turn 18 until late Freshman year and my parents never had to fly in to sign anything. There many in my situation, without this as an issue. It was under 16 that ran into issues.

As noted, CMU does have a program for this and it admits very few students. Read the description at https://www.cmu.edu/admission/admission/application-plans-deadlines

She’s going to a private school, although not an Ivy.