By this I mean is it possible for me to wake up, not remember a thing of the dream, and then remember some of the dream later on in the day or week, maybe even months?

I'm wondering this because I was listening to some relaxing music and I fell asleep, I then woke up with no memory of my dream, I didn't even remember falling asleep. Just to make sure when I woke up I did a couple of dream signs to make sure I was actually awake.