We almost certainly don't see Faith's first murder. I even see fans who take for granted that Faith only ever murdered one person (the volcanologist), but in fact we see Faith murder on camera for the first time in Choices. She seems very cool about it, giving the impression that this isn't the first time she's intentionally ended a human life. Even looking at Graduation Day Part 1 in isolation, there's no reason to believe this is Faith's first murder, and plenty of reason to believe it isn't. Again, she's very cool, and she tells the professor "I'll make it quick," as if she knows what she'd doing. When Buffy see the newspaper article about it, she immediately knows Faith committed the murder. She explains that the murder is "One of her pieces. I recognize the brush work." "Pieces", as if Faith has had a few of them. Later in the episode, during their fight, Buffy says to Faith, "All that killing, you afraid to die?" The line certainly implies that there was more than one murder and one accidental kill. The assumption of some fans that Faith only murdered one person has no basis in the text.
It is interesting to me that Faith's first accidental kill is a huge deal - a whole episode devoted to the immediate fall-out - but her first murder is possibly not even referenced or shown on screen. When did Faith cross that line?