Yes baby teeth will eventually fall out on their own without the need to pull the teeth or take the child to a dentist.
Most children will lose their baby teeth between 7 and 9 years of age.
I started losing my baby teeth at around 8 years of age and they fell out on their own without needing to see a dentist.
I also pulled some of my own baby teeth out when they became lose enough.
So if the child's teeth become loose enough you can sometimes pull the loose baby tooth out gently when it becomes loose enough.
Or you can just let the baby teeth naturally fall out on their own and they will without harming your child.