How does a photon experience time and the universe?

I don’t think this question really has an answer. A photon, of course can’t think, so what you’re really asking is “what would the world look like if I could ride along with a photon?” But you can’t: special relativity guarantees that anything with mass always moves slower than light. AFAIK, there’s no way to build a sentient being out of photons, so we will never be able to ask what it’s like, either.