It depends largely on how well you did during your first-year in law school, whether you are on law review or moot court, and whether you went to a solid undergraduate college and how you did there. There are plenty of graduates of non-first tier law schools at most BigLaw.
There isn’t as much stigma of graduating from a non-first tier law school at BigLaw as you might imagine.
Go check out the “Our Attorneys” sections of BigLaw websites. You should see a decent number of attorneys who have graduated from lower tier schools.
You would have more than just a realistic chance if you are in the 10% of your class and on the law review, no matter which school you are attending.
In my experience, some of the best associates are from second and third-tier law schools. They seem to have a chip on their shoulder because they have something to prove to their elitist comrades.
Excelling at a law school is sometimes a much better indicator of the potential for being a successful associate than merely doing well in the undergraduate school and the LSATs. Law firms know this, too. Thank you for your question. Good luck with your search!