At what age does a child develop his ‘I’?

Answer

You are actually asking two questions: the development of the ‘I’ and the development of a ‘thought’. A thought is a reflection = reflection on an experience. The child experiences first as an I and only later to think as an ‘I’. According to the French psychoanalyst J. Lacan (following S. Freud), the child experiences itself as part of the mother and must gradually withdraw from it. In addition to the word ‘mama’, it soon learns to say ‘no’. At that moment you can speak of an ‘I’. But biologically you can speak of an ‘I’ very early on: in the womb the baby is already an independent individual. The very beginning of ‘I’. And so it is also recognized by other people. Even if they do not yet know whether it is a boy or a girl. It will be different from the parents. And even if one were to clone one day, it would still be a different individual.

Conclusion:

Distinguishing the experience of oneself as ‘I’, autonomous individual; as seen by others as an individual person; as self-consciousness.

That last one is a gradual process of differentiation with regard to other persons: I am me and not like you, but can also disappear again if people become demented, for example.