This is a late night thought, and I apologize if it's something many have already thought of. Did at least one photon go straight out from the origin of the big bang and continue at C until now? If so, would that be considered the master clock of the universe?
Photons were first created around 10 seconds after the Big Bang, when particles and anti-particles annihilated. For 380,000 years, the Universe was hot enough that all matter was ionized, and since on top of this the Universe was very dense in the beginning, the mean free path of photons — i.e. the average distance traveled by a photon before it interacts with a particles (usually an electron) — was very small. When the Universe was 380,000 years old, the temperature had fallen enough that the electrons could remain bound, so the Universe became neutral and light could stream freely. This released what we today observe as the cosmic microwave background, of which roughly 90% has traveled ever since without interacting with any matter.
But, the probability of not having scattered on an electron before recombination is so extremely small, that probably no photon in the observable Universe hasn't done this.
However, the Universe is probably infinite, so no matter how small a probability, there will be infinitely many photons that were created 10 seconds after Big Bang, and which has traveled freely ever since.
Or no, actually:
But, as pointed out in igael's answer, a photon cannot act as a clock. Since photons travel at the speed of light, they have no reference frame. In a popular way you could say that they experience infinite time dilation, so for them no time has passed since their creation.