Physical20activity20to20prevent20obesity20in20young20children3A20cluster20randomised20controlled20trial20–20Reilly20et20al.203332075773A20104120–20BMJ
A Scottish study offers an answer to this question for pre-schoolers.

Even 4 year olds are obese and often sedentary. Sedentary!

So 545 kids in 36 nursery schools got physical activity programs three 30 minute sessions each week over 24 weeks. Their parents also got encouragment, and program guides, and the control group of pre-schoolers got ther usual curriculum.

Result: no effect on their weight (BMI) or their habit of activity. But movement skills did improve.

Lesson: just as in adults, weight loss is first about what you eat. Weight loss maintenance is about both, but as much about exercise as food.