[Hammy992]

Hey!

It sounds like your hammy has settled into his new home well and is enjoying his cage.
If there are plenty of fun and interesting things for them to do inside their cages it is normal for them to not want to come out to play every day.
I'm not sure whether you have a cage where you can just pick him up but as Souffle suggests still give him the option to come out when you see he has had time to wake up and looks nice and alert. If the door is not too high up you could set up a playpen around the cage every night with a small animal ramp to reach the floor so he can wander out to explore in his own time (do supervise of course as they can escape pens!), or even offer him a container or tunnel to hop into instead of your hands.

With my hamster I always offer him a tub of bathing sand for him to climb into and he associates this with outside playtime and getting treats! For some reason he doesn't like climbing onto my hands to come out although has no issues at all outside of the cage.

As long as he has a good size running wheel and other ways to get exercise he should be OK to choose his playtimes as he likes.