The Lorentz factor diverges when the speed approaches c. Because of Length contraction and time dilation, both the distance and the time will appear to be 0, from the "point of view of the photon".

(the photon is "in 2 places at once" only from the point of view of the photon, and it doesn't think these places are different, after all they are in the same place! This among other things is why the notion of an observer traveling at c, rather than close to c, is problematic)