Upon emerging from pupa, beetles do not immediately eat and move around. Instead, they undergo a period of dormancy, during which they must harden and adjust their new body for the outside world. It is advisable to not handle the beetle as much as possible during this period since they are fragile and prone to stress.
Unlike active beetles, dormant beetles don't require much management.
This is the main method I use to take care of dormant beetles:
1. Place the beetle in a container with some moist paper towels
2. Cover the beetle with moist paper towels
3. Place the container in a cool, shaded area
4. Check the container about once or twice a week. Beetles that are beginning to become active will move around the surface a lot more. But most importantly, they will shred the paper towels in the container. 
5. Once you notice these signs of activity, try giving the beetle a slice of banana. If active, it will feed on the banana. If not, wait a few days and try again.
Few things to keep in mind:
1. Containers housing dormant beetles do not need to big as they don't move around a lot.
2. Don't let the insides of the container dry out but don't make it too wet either.
3. Most beetles usually stay dormant for 1-3 months. Warmer temperatures tend to make the beetle break out of dormancy faster.