Toddler entering childcare center.

It is normal for children to fall sick when they first enter preschool as they are exposed to more things in their surroundings as before. Additionally, it is normal for children to take at least a month to adapt to their new environment and depends on their age as well. But it is common for children to cry when they first left their parents, and check if the teachers how your child are adapting throughout the day such as nap time and playtime. This will be a better gauge of adaptation than what you see because there's a tendency of children crying when entering and crying when their parents came to fetch.