You will probably have to cut your teeth on musicals whether they're your forte or not. As you have seen, they are a lot more common than pretty much any other thing to do if you want to be an actor.
Another option is Shakespeare if there's any place near you which is doing dramatic legitimate theater. Yet another option is comedy troupes.
As a full-time student, though, your chances are slim. Not zero, but slim.
In order to improve your chances not just for these kinds of roles but for future roles, consider taking classes. Dancing, singing, public speaking - any of those could really help you.