I think it depends on the individual.
Some people never have deep thoughts, emotional depth and intellectual even when they are 40 and some people have it already even when they are 8.
It depends on the environment you live in and the experiences you make and age doesn't equate strictly with any of that.
As for hormones, we have all kind of hormones from testosterone to epinephrine and cortisol since we're babies. Puberty is not a process by which an hormone-less body becomes hormone-full but the last visible stage of a hormonal activity linked to tissue growth started in the first years of life.
In other words if we look for an objective anatomical and physiological way to standardize the kind of maturity, knowledge, emotional depth, empathy we should aspect a child to have we won't find any. It's a subjective and environment based thing. Even Piaget has been proven wrong, since his studies on "cognitive development" (that lead him to theorize that cognitize development is strictly linked to chronological age) dealt with children of a single social class of a single city of a single nation. When researchers started to mix children from different cultures and social classes it became clear that their level of maturity and cognitive ability depended on the environment they were growing, the right to explore the world in their own way they were granted and the responsibilities they were given.
The modern society infantilizes children so that we almost forget the potential we are supposed to have at a very young age.
You can for example notice that poor children are way more mature than whealthy spoiled children and often more mature than wealthy spoiled adults. This is not a bad thing. This is not exposing them to real life too early, this is letting them be people rather than semi-conscious puppets living in perpetual triviality and kept under a dome of glass away from the real world, ready to grow with lot of fears, paranoias, hatred and superficial outlook of life (what do you expect from someone forced by his/her parents and teachers to live in a humanless surrogate of the world rather than in the real world?)
Some children are capable of more maturity, intellectual and emotional depth, insightful outlook and empathy then their parents, and some children are not. Even though, usually, when children are like that their parents are like that too and viceversa. There are indeed young performers who can render the profound emotional content of a piece better than their adult counterparts.