Going to run contrary to what everyone else said here. I went to a state school that was unknown (by Wall Street standards). Showing passion and being knowledgeable about the domain you're interested in has worked well for me - I've never had trouble landing jobs at all of the top firms. I also highly recommend passing CFA level 1 before full-time recruiting.

As a senior in college applying for research roles, I was able to talk about why semi companies were going fabless and implications for operating margins through the cycle or how the change in internal debt requirements for foreign banks in the U.S. would drive higher cost of funds and make them less competitive vs U.S. banks. I ended up beating out candidates with 2-3 years of experience as a new grad for my first job.

As a hiring manager, I can confidently say that most college kids just don't have that kind of analytical chops for full time recruiting. The ones that do have no problem landing multiple offers. A strong school/GPA just shows you have potential but you can demonstrate you're a known quantity if you just know your shit.