Accepted to AMEP but want to change to ME

Hey! So I just got accepted into the university of wisoconsin-madison for AMEP(applied math and engineering physics and it’s in the college of letters and sciences);however, I believe that I want to pursue engineering. How hard is it to change schools? (btw I am an incoming freshmen). And if I hypotheically don’t get into engineering for the first year, will I be able to transfer to the CoE the second year?

P.S. I sent them an email and they said in order to be reconsidered to CoE, I must send them an email stating why I want to change schools. Do you think I actually got a chance?

STATS—
GPA: 3.95(don’t have a weighed GPA in my school)
SAT: 1370
OOS

Thank you!