I think learning about death is a gradual thing, rather than a sudden realisation, which is why I doubt many of us remember it as a specific moment - but instead early life experiences such as pets or grandparents dying & being told by our parents that they have gone to heaven or similar euphemisms form a foundation for this understanding. Then as we grow up we simply come to understand it as an inevitability of life without ever dwelling on it too much.
I think this is a good description of what happens in The West. In The East they definitely are more conscious of it than us whereas I don't believe we give it too much thought.
Having been in the doctor's room being told you have cancer and the walls collapsing in on you though I don't think anything can quite prepare you for becoming instantly conscious of your mortality. Then I lived in a sort of state of shock for a while before I had an experience one night of what some have called "The dark night of the soul" which was pretty gruesome. However after that I had acceptance and to this day I now have absolutely no fear of death.