What I understand is Sakkaya means
Sakka+kaya meaning “Good”+”Actions”
It means that people have a view that whatever action is done to please oneself is good and worth it, so it is good to acquire worldly things for oneself, here the sense of “self” arises.
The baby’s thought process is influenced by its parents/environment and also the baby’s past gati,when it grows and starts to understand things.
I think initially Sakkayo is not there in the baby because of its low intelligence and less mental defilements, but with time it starts to arise.
