In some Christian circles it is commonplace to be able to share the time, place or date of when you "were saved". Some Christians, like myself, don't have a moment in time that I can point to and say, "this is the moment". But that is not the reason I do not say "I was saved". Mine is more theological rather than biographical.
I believe that salvation has little to do with what I do, say or feel. If there was a time that I "was saved" it was in the life, death and resurrection of Jesus. I do not say "I was saved" in some moment in my life because God's action of reconciling all things predates my existence and actions.
It may also be worth noting that what we are saved "from" is a large topic of discussion. And, as far as I can see, there is no one thing that everyone needs to be saved from. There are a lot of things. While some need to be saved from our pride, others need to be saved from our self hate. Some of us need to be saved from starvation and others of us need to be saved from slavery. To say all this is "Sin" may be generally accurate it also removes the specific need. God so loved the whole world and in this love God saved the world.
The good news is we are saved and we did not do anything to earn it. Now, we get to live in thanksgiving, humility, gratitude and grace. And we have faith that living with the posture of thanksgiving, humility gratitude and grace leads to life eternal.