In a fictional universe, yes, we would just not know for a few minutes.
Fortunately astronomy is already a well-developed field, so we'll know when the sun is going to "go out" or "explode" at least several thousand years before that event actually happens. For those sitting around on the Earth at that time, they will have to wait 8 minutes before they notice anything.
A much more cool realization is that you can look up at the night sky and be seeing light that is millions, billions of years old. Astronomers recently announced that they've observed several billion year old light (the oldest light known) from a galaxy formed in the early universe.
Fortunately astronomy is already a well-developed field, so we'll know when the sun is going to "go out" or "explode" at least several thousand years before that event actually happens. For those sitting around on the Earth at that time, they will have to wait 8 minutes before they notice anything.
A much more cool realization is that you can look up at the night sky and be seeing light that is millions, billions of years old. Astronomers recently announced that they've observed several billion year old light (the oldest light known) from a galaxy formed in the early universe.