When you apply, do you apply to major ?
For computer science, do you apply / get acceptance to general engineering like TAMU or apply / get acceptance to computer science ?
You apply to Rice. You tell them what you want to major in, but it isn’t binding. And you can change your major literally whenever you want.
So you put School of Engineering as your intended school of study, and Computer Science as your intended major, but you get in to Rice and can switch to anything other than music or architecture. It’s as easy as filling out a short form.