[Is] the photon at its starting and its final position at the same moment?
At the same moment with respect to whom? That is the question one must always ask in relativity.
The answer is: no, emission and arrival do not occur at the same moment with respect to any actual reference frame. However, as we consider an abstract sequence of reference frames that move faster and faster approaching speed c in the same direction as the photon, we find that the time between the emission and the reception is shorter and shorter.
Haven't had one of these for awhile. This thread is for questions or comments that you've felt silly about not knowing/understanding. Let's try to exchange info that seems obvious, knowing that due to the illusion of transparency it really isn't so obvious!