Is it possible for a sun to be older than its biological matter?

We have only one observation of biological matter in the universe, and no clear idea about ages. It is not clear what you might mean by "it's" since there is no particular connection between the sun and biological matter except that we need the radiation.

The ancient Greeks and Egyptians recorded that the Earth had two suns before the one it has now, and one of them was green. But that does not suggest anything about ages.