I definitely remember things from around ages 3-4 which are absolutely not traumatic. For example I have fond memories of both my great-grandmothers who both died when I was 4. I remember spending time with them. I also have other memories from that time, just can't be sure about the exact timing. The ones with my great-grandmothers are impossible to be from later.
And I definitely have complex memories from around 5-6 years old, which do qualify as "gaining self consciousness". Of course I can't pinpoint exactly when that was, but it's a significant memory I have... the exact moment when I realized these things.
Memory is sometimes considered as a network where "pieces of memories' are pulled together to create a memory for "present you". Traumatic memories from the past aren't that traumatic after many years after, and are being changed every time when being recalled (that's one of the theories).
You can lisen to recent Lex podcast with Charan Ranganath, i got it timestamped when talking about child memory: https://www.youtube.com/watch?v=4iuepdI3wCU&t=885s
And I definitely have complex memories from around 5-6 years old, which do qualify as "gaining self consciousness". Of course I can't pinpoint exactly when that was, but it's a significant memory I have... the exact moment when I realized these things.