What is minimum age to pay taxes?

There is no minimum age.

Theoretically, a new born infant might have to pay taxes.

This could happen if, for example, a doting grandmother gives the infant some property in a Uniform Gift to Minors Act (UGMA) account and the property generates income (interest, dividends, rents, etc.). Certainly, if you are old enough to earn money, you are old enough to pay taxes on it.