I think it depends on what you mean by "really matter." Matter in terms of what?
In terms of future employment, I think the answer is mostly no. Unless you go to an Ivy league school or some other well-known university, it really doesn't make much of a difference to employers. They care more about whether or not you have the experience and skills to do the job. This is why things like work experience, internships, and extracurricular activities matter so much.
The biggest difference in universities is in how much they facilitate that process. Some schools provide plenty of internships, jobs on campus, excellent career centers, certificate programs, academic projects, student organizations, rigorous coursework, study abroad programs, and other opportunities that help you build your resume and facilitate your overall growth as a person. Other schools...don't do this very well. That doesn't mean you are doomed to fail--it just means you have to put in a little more work in finding those opportunities compared to a student whose university just provides them automatically.
Students that generally get into the top tier schools have better employment rates because they are naturally hard-working, resourceful, and high-achieving people who do the extra work it takes to make themselves a competitive candidate for employers. I would say that employment success is less about the school you go to and more about the type of person you are.
If what you mean by "really matter" isn't so much future employment, but more a general, "does this really matter in terms of my entire life" kind of meaning, then in that case, the answer is yes. The university you go to can definitely affect your life a significant amount in terms of the overall experience and fit. For example, say that you are a high-achieving student who is eager to explore a very niche interest, meet many different people, and travel all over the world. Then you (for some terrible reason) end up going to a small, local university where your niche interest isn't available as a major, all your classes are full of the same people you grew up with, and there isn't enough funding for study abroad programs. You are going to have a very miserable 4 years.
Try to do some self-exploration and find out what's most important to you. What do you want to get out of university? The choice does matter to an extent, but it isn't always everything. You want to find a university that is a good fit for you, but no university will ever be the PERFECT fit, which is where you'll have to do some of the work.
YES it does. If it didn’t matter, you could simply go to any college, graduate, and have the same post graduate success in the job market as anyone else. That is not the case.
I have personally visited well over 100 college campuses across the United States. There are BIG differences between colleges that you should take into consideration.
Typically students who go to top tier and highly competitive elite colleges do far superior in the job market when graduating from college.
And, some colleges do an outstanding of graduating their students in 4 years or less... where other colleges are so crowded that it might take 5 1/2 years to get the required classes to graduate.
Some colleges offer generous financial aid packages or scholarships whereas other colleges offer little or no financial incentives.
Some colleges offer superior programs in engineering, business, and sciences with outstanding state-of-the art facilities and incredible professors. Other colleges have old technology and outdated facilities / outdated professors that do not prepare you for today’s competitive business environment.
Some colleges have classes with over 1000 students. Other colleges have classes with 12 students. Some college have 60,000 students. Other colleges have 2000 students.
Some colleges have tremendous pride and alumni support where you will be proud to wear the school’s colors and cheer on the mascot. Other colleges have little gravitas and indifferent alumni.
Some colleges have football where 80,000 people convene to the campus on Fall Saturdays. Other colleges have rowing.
Some colleges have gorgeous campus grounds and a college town vibe that is so fun and appealing. Other colleges are surrounded by parking lots and weeds.
I could go on and on. But, your choice of college does matter.
Another factor to consider is the life experience a college can give you. I went to a school that does not provide much post college life experiences. Some of my friends who went to a big ten school, are enjoying plenty of alumni activities. Sporting events, bars that affiliate with their schools for games and even alumni book clubs etc.
What "really matter" means to you is something you need to explore personally and professionally.