Neutrinos have been observed originating from a supernova just as the light arrives. However, a neutrino does have a small, detectable mass. If its arrival coincides with light from an exploding star, how is that possible?

Neutrinos are actually emitted prior to the explosion. They have a very small, but non zero mass. Being that small, any push sends them flying off at near the speed of light. Neutrinos travel slower than light, but not greatly so.