Your question is the one that Einstein pondered for long time and from which Special Theory of Relativity was born.
He wondered what could happen if you travel at the speed of light how would you see a ray light. The problem was that according to Maxwell's Electrodynamics, explained light as oscillating $E$ and $B$ vectors along space and time, so as a wave. But then you would see $E$ and $B$ oscillating statically, which was not observed in nature thus contradicting experience.
There lies the problem with that reasoning, which lead to admitting that light should be invariant for all inertial systems, and further to STR.
Baring this in mind, you can see why a photon cannot be thought of as a classical particle, and is only a working concept in Quantum theories where velocities and positions cannot be simultaneously known to infinite accuracy, thus paths are inconceivable.
So not in the scales where light behaves classically, nor in those where it does not, can a photon it be conceived as a standing in rest, because it contradicts observation.