Other than the First-Year Glynn Family Honors Program invitation, you might want to encourage your student to have a serious look at the Sorins Scholar program at Notre Dame, which is just excellent:
https://cuse.nd.edu/sorin-scholars/our-scholars/
Admission to the scholarship program is based on a competitive application process towards the end of the First-Year of studies at Notre Dame. Information on the application and other aspects of the program are included here: