in my opinion a boy should start going to shul on shabbos when he is 8 years old for at least part of the davening.
If someone can bring him to shul for the last half hour in the beginning and eventually by the time he is 11 and half you work him up to staying the whole 2 hours for shabbos davening.
If their is a shabbos drasha never except him to stay in for that until he is over 13 and even then it may be best let him go outside.