A supernova is not something that happens with little forewarning. I would guess that you would have hundreds of years of warning. That is one of the two plot holes in the 2009 Star Trek movie. The other being where did a “simple mining ship” get so much weaponry?
The biggest hole in Faux Trek was allowing that Star Wars fanboi Abrams anywhere near it.
The supernova in the movie was caused by the red matter (whatever that is) and the mining ship got all its bling because it travelled through time collecting stuff.
That’s my story, and I am sticking to it. :-)