Judging by the content of General Hux's speech, it seems to me like he's implying that it's the first time:
This fierce machine which you have built, upon which we stand…
Also, he's turned it into a pep talk event; it wouldn't have as much punch if it were the second time the weapon had been fired.
Also, how do you fire it (in any direction) without giving yourself away?
Edit:
I know this is a little late, but I just realized that the movie itself contains some pretty clear evidence that this is indeed the first time that the Starkiller has been fired at full power. It's the scene in which a swath of forest gets razed by the force of the blast.
These are apparently large, mature trees that take decades to grow, definitely much longer than the time it took to build the weapon and maybe even before the First Order was created. If the Starkiller had recently fired, then this scene would be a desolate moonscape, not a real live forest.
Note, however, that this scene does not disprove the possibility that the weapon has been fired before at lower power levels. We don't know what other sections of the forest, such as those closer to the power, look like.