Are there events in universe which we receive first from their neutrino's instead of their photons?

Yes. When a core collapse supernova happens, it takes a few hours for the shock wave to reach the surface and "break out" (when we first "see" it). Meanwhile, the neutrinos can escape nearly directly once they reach the top of the core.

Of course, as you wrote, photons travel slightly faster, so if the SN is far enough away, the photons might overtake these neutrinos. However, I have not done the calculation to see if the universe is big enough.