I've literally never woken up and remembered anything, even within seconds of waking up. I've even tried because I know that other people experience dreams. It's just a complete blank from the moment I fall asleep till the moment I wake up. Just nothing.
People typically remember their dreams when they wake up in the middle of one, and usually then the REM sleep stage. I remember some guy studying this, got his assistant to wake him during REM and found the dreams were pretty vivid when this happened.
Maybe you're just enjoying a sound sleep and waking at the "right" time.
I don't think that is it. I'm in my 50s and have multiple kids. I've been woken up many times.