I looked at the web sites of a number of universities in New England and New York, looking for FYE programs. I did find one that I don’t think was mentioned above:
SUNY Binghamton’s FYE program: First-Year Engineering Program | Engineering Design Division | Binghamton University
Here are the others that I looked at just now. None of these appear to have FYE programs. Of course, most have some “common courses” and flexibility to change majors, because many engineering students do change majors. Flexibility is not the same as a FYE program, but it can be workable.
BU: Nope
UConn: Nope
Cooper: Nope
URoch: Nope
RIT: Nope
Buffalo: Nope
RPI: Nope
UNH: Nope
Northeastern: Nope
UMaine: Nope