Good questions. Tolstoi, for example, claimed that he remembered himself lying in the cradle. There are some other examples of very early long term memory.
It’s almost impossible to memorize such early memory as in Tolstoi’s case. How could one remember ‘lying’ before the concept of lie is created in one’s memory?
Similar reports might be a result of reconstructions of memory from recalls of parents or grandparents rather than an original personal memory before the long term memory is ready as a young baby.
I am sorry for my english in advance as I am not native speaker. You can read my view on this question below.
The answer differs in relation to age of child and developmental stage of his brain. I agree that long-term memory is somehow dependant on development of parietal and temporal areas associated with language skills and spatial imagination but it is more complex than that.
Let's begin with child younger than year. He is primary developing brain areas processing motoric and sensory information. Character of his memories is visual since infant can process experience and perceived data from environment but mainly in unconsciousness level. He can not verbally explain them as the declarative memory is not developed, so there is almost no possibility to revive the memory after longer period of time. It is also called childhood amnesia. So I think that Tolstoi did not remember himself in the cradle. I think that even if we were able to remind some pictures from earlier phases after full development of our brain, it would not make any sense to us. It was completely different type of perception adapted to our recent state and our perception keep on changing according to life experiences.
But what if we are talking about deaf people? They also got their own language but I think the way they perceive reality and think is different.