There is at least one known exception: neutrinos from a supernova. (Don't get too excited, this doesn't contradict Einstein, as we'll see.) In the hot, dense core of a supernova, photons will scatter around for a while before escaping. Neutrinos, which interact much less often than photons, and travel also more or less at the speed of light, get out basically right away. The difference can be as much as a few hours! Of course it's the high-energy photons that are more dangerous, so the neutrinos are really more like an early-warning system.

See e.g.: https://en.wikipedia.org/wiki/SN_1987A