Yes, when I was a child I had memories from when I was actually in the cot.  As I grew older they were lost.  But one I still remember, because I 'renewed' while still young, after finding an old keepsake.  This was of lying in my cot, reaching for the pullstring of my beloved little blue plastic music player, that was attached to the top rail of my wooden cot.  I loved the music.  Of course, this is just a memory of a memory now, and doubtless it's been warped by time.  But as I say, I do remember reflecting on the other memories I used to have and I remember having them and not thinking that anything unlike my reality of the time was in them.

I was good at remembering things until adolescence.  I don't know if it was just getting older, or all the booze and weed, that has reduced my capacity.  My long term memory is average now, and my short term memory isn't great.