How long do I have to wait (ingame/real time) until a new born child will become a laborer?
Children advance at age 10, becoming either Laborers or Students.
They will only become Students if there is a school with space available. Students then become Laborers at (around) age 17.
Doing the math, on average, it's 2 years (or 24 seasons) per 10 "age", and 3.4 years (or 40.8 seasons) to age 17.