Actual Time Scale: Four Years
We know that we're talking about a science fiction universe in which both fire and sound are possible in the vacuum of space. Oh, and that literal wizards can move objects with their minds. That, too. We're not exactly expecting Stanley Kubrick levels of realism here, but most of the physics of our world -- such as gravity -- seem to remain more or less intact in the Star Wars universe. So for fun, let's imagine how long this event should have taken.
First of all, we're assuming that whatever the Starkiller beam is made from, it's moving no faster than the speed of light. It's true that spaceships in Star Wars can travel faster than light, but a beam of pure plasma or energy or whatever probably doesn't have a hyperdrive installed on it. We also know that Starkiller Base isn't in the same solar system as Hosnian Prime, because it needs to vacuum up a star before it can operate, hence its creative name. And the star in the middle of the Hosnian System is still shining at the time of impact.
R.I.P. Manatee-Pug-Face Man. May you live on with your 12 unnecessary action figures.
Best-case scenario is that Starkiller Base is orbiting the very next star over. We don't know how far that is, but we know how far our sun is from its nearest neighbor, Alpha Centauri -- a little over four light years. This means that, even if Starkiller Base is as close as it can possibly be to the Hosnian System, it still likely takes a matter of years from the moment they pull the trigger to the moment they hit their target.