He has lots of nice hidey places and tunnels in there - I can understand you not wanting to add too much bedding yet if he's a bit shy and not tame.
With offering a tube I meant as a kind of taxi
Rather than moving one that's already in his cage (although that could be an option). I used to put it at the house entrance, with a bit of cucumber at the far end, and it would tempt the hamster to walk into the tube. That way you can lift him out for some socialisation and taming. I always find it works better out of the cage than in it
Once he's got used to you and being handled he'll probably be out and about more in his cage. I'd maybe add a large shoe box house at the left hand side and put it over his current nest - he'll like that as it'll be dark inside. And you can lift the roof off to check on him. The current bendy bridge he's nesting under would make a good tunnel entrance (so it's even darker inside) and also a ramp onto the roof. If you cut the base out of a shoe box, keep the lid as a lift off roof and cut a hole for a door on one of the long sides (ideally towards one end so the other end is darker).
I'm sure he'd be tempted out through the house door by a tube with a smelly treat at the far end