"This/that is a first", colloquially, is an idiom that means "this is the first time this has ever happened (to me)." It gives force to the idea of experiencing something for the first time, in a short, succinct manner. Essentially a first means "the first time/experience/occurenceoccurrence."
If it were "This is the first," it actually wouldn't make sense, because that phrase begs the question: "The first what?"