Not really. 'As early as' needs a more precise term to follow it, such as a specific age or time. 'Childhood' is too general a term. Also, we know from the beginning of the sentence that we are talking about children, so the word 'childhood' isn't telling us anything new.

Я бы заменила as early as in their childhood на very early - а то получается, что "дети учатся уже в детстве". Но тут надо пересмотреть смысл самой фразы, а не грамматику.

Thank you, Morghanna.

The sentence could be posed: children learn love and compassion through communication with pets in their early childhood.