Whether you can die or not is entirely up to how you define yourself. If you define yourself as a body and a mind, which have a begin, then yes you can die. However if you take a U-turn in your spirit and see yourself as consciousness instead of only your body and mind, then no cannot die.
How do I know this?
Be present and see yourself as you are and you shall know this as well.
There is something accompanying you, it has always been with you. Something remarkably exquisite and intangible by your mind and hands. Something which in fact is who you are in you essential nature.
This awareness is your primordial self, it cannot die, for it was never born. It cannot even fade, for it is perfect. It is pure existence.
You cannot die, even if you think that you can die, because you are not merely your mind and body. You are that light which gives life to all things including the thought of your own possible mortality.