If one applies to get into Weinberg, and is interested in math/physics, then decides one wants to do engineering, is it possible to transfer into McCormick? What if one decides that one wants to transfer into McCormick before school starts?
https://www.mccormick.northwestern.edu/students/undergraduate/advising-registration/ says that “Northwestern students interested in transferring into or out of McCormick should contact” a person listed on that web page.
Perhaps you want to contact that person to find out what the procedure is and how difficult it is.