My earliest memory was of my first day of pre-school when I was three years old. I was playing with one of the kids when he by accidently broke my tooth. I remember crying hysterically and my mother running on to the play ground and picking me up. My personality is similar to how I was back then. I forgave the the kid very quickly. I still don't tend to hold grudges. However, my identity is very different; that part of my life seems so distant from my current self.
I think the memory is fixed in the mind as it was slightly traumatic and impacted you severely which makes instances fix more easily in the long term memory.
Mine is similar as I too was in preschool and it was one of my first experience with the sense of achievement which is also more easily fixable in long-term memory as it has a major impact on you.
It makes sense that you would remember that because it had to have been very traumatic at the time. Typically these traumatic experiences are what stick in your long term memory. These memories are usually fragmented and don't form a continuous memory to the present.