When does an individual begin to feel esteem and gain self respect?

Depends on the person.

There is no exact time that this will occur, but it's a lot more likely to happen after high school. High school is the time in life where your self esteem will be at it's lowest, most likely, and you'll be wondering 'what do others think about me?'

Afterwards, people normally start to realize that it doesn't matter what others think, so they start to do what makes them happy.

When you find that thing that makes you happy, you gain self exteem and self respect. (: Normally, if you're good at something, it'll have the same effect.