For instance, there is often talk of the Black Hole Era, where all the suns have died out and only Black Holes are left. If life was to evolve to sapience in that era (leaving aside questions of if it's possible for life to originate in the Black Hole Era), how would they ever know that there once were stars in the universe? It would surely be impossible to derive that conclusion from the information they will have available to them.
For such beigns, and for any exotic life forms, it would be impossible to study the past. That's for sure. So I agree with that.
So all I do is ask you to consider that we could very well be in that same situation. What events have we not witnessed in the earlier era of the universe that we cannot possibly know about by observing what we see in the sky today?
Some stars have died long ago and some were born. As time goes by, it becomes more and more difficult to investigate the events from the past. But that's not the real issue for today's astronomy, precisely cosmology. The main problem is to understand the early stages of the Universe, because the Big Bang theory is reliable. It's just that we barely know what happened in the first seconds.
As for the origin and death of the universe, I simply can't believe logically that the universe began with a Big Bang and will end with Heat Death. There are two options, maybe more than two but I can't conceive of them: that the universe is either infinite or it is finite with a definitive end and beginning. Both options are not satisfying to me even if we were to definitively prove one or the other, but logically it makes more sense for the universe to be infinite because how can something come from nothing? But an infinite universe is also something I simply can't understand, but I suspect that is because I am a finite being with a beginning and an end. I can, however, accept logically that the Big Bang and Heat Death could be a finite event in a greater infinite landscape (multiverse theory).
It's good to see different views on it, doesn't matter if you're not a physicist. I stated the inevitable heat death of the Universe because thermodynamics is a well established theory. That doesn't mean that something different can happen. Science is for debate, for sure. After all, we don't know what we might find out in the future =)
Something I forgot to say in my previous comment is that immortality is not for everyone. Dying is bad, of course. But by dying you make room for someone else of the next generation =)
Having said that, I found the answer "curse" to be more accurate than "gift".