The memory develops after birth. A baby starts by registering how it should move. From around the age of three, a child can register events which form part of its life story, to be recalled in later life. But emotional events such as traumas are possibly registered much earlier as stray facts. These can elicit reactions, although you can’t retell them.
If you cut your finger the pain appears to originate at the site of the wound. But that is misguided. Pain is an emotion that is generated in the brain itself. Pain is always in your head.