The first day is an especially difficult time for you and your child. We do not mind if you stay for the first half hour to help him/her settle down. However, when you are ready to go, tell your child you are going and that you will be back. THEN GO.
A quick break is much easier on a child, than a long lingering goodbye.
Please feel free to call and check, throughout the day, if it puts your mind at ease. It’s better than sitting at home and worrying.