You are correct that a photon exists only instantaneously within its own Relativistic reference frame. This was a key insight of Einstein's. For a photon emitted from a star, propagating across intergalactic space to a camera at an observatory on Earth, within its own reference frame no time elapses and no distance is traversed.
It certainly has a physical existence. Four-dimensional spacetime is sometimes understood as a "block Universe", with the whole of its past, present and future forming a single continiuum. However, in the Relativistic model, the exact direction and rate of passage of time are not absolute, they depend on the particular observer who is measuring it. Any observer must follow their own timeline too, and can see only what is within their "light cone", the region of spacetime which is accessible below lightspeed. The rest of the block universe is inferred only because the laws of physics assume a symmetry which requires its existence. A photon follows a straight line or "geodesic" across the block landscape. So if the block universe exists and can support structure, then the photon also exists within it.
To the photon, neither space nor time exist. Yet it must undergo an absolutely fixed and finite number of oscillations (i.e. the same for all observers) during its journey, so it has some "knowledge" of its adventure and is more than just a structureless point.
So yes, on that basis the photon exists all right, but the nature of its existence is not easy to unravel.
For example we may want to cut an instantaneous spatial slice across block spacetime, call it "now", and declare that only "now" truly exists. But where the slice falls is relative to the observer. If I cut the slice relative to myself, the photon is a point in an identifiable location (or maybe a probability distribution across a certain patch of space). But relative to the photon itself, block spacetime has no extent, the slice falls... well, let's think about that.
Perhaps a clue is to be found in twistor space, a transform of block spacetime formulated by Roger Penrose, and which he has described loosely as "light-ray space". In this model, the photon is a point in twistor space and any given point in block spacetime, through which it has passed, is smeared out across twistor space, among all the other photons which passed that way. Any slice of "now" must be smeared out in similar fashion, as all the photons it crossed paths with on its journey. Twistor space is of major importance in high-energy particle physics, where it greatly simplifies the calculation of particle-particle interactions. That is to say, particles which met at a common here-and-now point in the block Universe.
All this is a "classical" or large-scale model of existence. On the quantum scale things behave very differently and the nature of existence has its own problems. According to the mainstream "Copenhagen" model, nothing exists except measurements and their probabilities. But that is really another question.