Unfortunately you will have an uphill journey, not impossible, but certainly harder. First of all you will need to network in order to get you initial interview, get someone to put you resume on the pile; this is a lot easier for target school students because of the alumni network and prestige of the school.
Now, once you have the initial interview is all on you, interviewers will be more concerned about your fit for the role. Unfortunately, defining fit is also an uneven fight as there might be a bias from alumni to prefer their colleagues (or people from schools they recognize from their own coworkers), so you will have to demonstrate distinctive skills, superior enough that interviewers will be more excited to have you than a colleague.
Once you get the job (or internship) it will be mostly up to you, I wish I could tell you that school you went to doesn't matter anymore but it plays a small role once you start working, but nevertheless talent, hard work, and a great personality are much more relevant once you are inside.