Here is a diagram that describes what happens when a photon hits your eye.
It is in two dimensions, one is time the other is space. The photon interacts with the electromagnetic interaction with an atom in the retina of the eye, where the electron which is bound in the atom goes to a higher energy level and the photon is absorbed giving its energy to the transfer. The consequent deexcitation will propagate along the nerves to the brain.
The time the photon started on the left is irrelevant with respect to the interaction which happens at a specific (space, time ) point, and also the velocity is immaterial.
What is important is the quantum mechanical framework, which is the framework of particle interactions. The Heisenberg Uncertainty Principle even without detailed calculations tells us that there exists an uncertainty in the exact four space point, because calculations give the probability of interaction, and for a given accuracy in the momentum determination for the photon and electron there is an indeterminacy in the position.
This of course has nothing to do with the "age" of the photon, or the time it took from its creation to reach the interaction point. The photon is an elementary particle and elementary particles do not "age". Whether it comes from the sun or from the desk lamp the probability of interaction depends only on the photon's energy ( frequency times h) and the atom it impinges on.