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.