Oh my goodness - ha ha - I looked at the photo and at first thought the hamster's head was sticking out of the top of the tank! Must put my glasses on
I think he has had time to settle in and a bit of time to adjust to the changes you've made, depending on how recently you've made them. Our last Syrian was also very shy, nervy (and a bit lazy) and would never come out at all unless I actually got him out for taming.
Whenever you last made changes in the cage, give it a week and then I would start with taming out of the cage. The best way to get him out would be in a tube or hamster ball with a nice smelly treat in it - eg a bit of cucumber or a very small bit of plain cheese (eg cheddar). It's how I always had to get our last Syrian out. Our current syrian is more active and confident and comes to the cage door when he wants to come out, which is usually about every 3 days. So they do like to have some time left alone as well.
Without a cage door in a tank he would show you in some other way.
Anyway - if you have a hamster ball it's easy enough to just lower that into the tank near his nest with a treat in and he'll probably just walk into it, then pop your hand over the entrance and lift him out in the ball, pop the lid on and carry him carefully in the ball to where you can let him out safely for some taming - you could either rig up a playpen area on the floor, or use the bathtub if you have one. Bathtub taming is good - the sides are high, they can't escape and you can add the odd toy or hidey place in there.
I am not a great fan of hamster balls for exercise - but it is useful to have one for transporting a hamster from one room to another safely, by carrying them in the ball, setting them down and taking the lid off to let them climb out in the new location.
Another way is a tube - with one end near his nest and the treat at the far end. This takes you being confident as when he goes in the tube for the treat you need to cover both ends with both hands to lift him out so don't jump if you feeling him pushing at your hands. If you're nervous he may bite (unlikely) then wear gloves when doing it.
You can't carry them far like that in a tube safely - I used to then put one end of the tube in the hamster ball (ie hamster ball didn't fit in the cage). If the playpen area is very nearby you can just put the tube down in that. If you have to walk toanother room - eg the bathroom, and you don't have a hamster ball, then put the tube down in a box or similar (high enough sides he can't jump out), and carry him in the box to the other room - put it down on its side so he can then walk out. I would still put something over the top of the box just in case! They can jump quite high.
They behave differently out of the cage than in it. Their cage is their territory. When in a safe area like the bathtub or playpen just let him run around and occasionally try and stroke him on the back with one finger. Wear gloves or use an old toothbrush instead of a finger if you're worried he might bite - again unlikely. He may jerk round as if to bite or warn your finger off, so wait and try again 10 minutes later. Maybe try this 2 or 3 times in the first session. Use your finger without gloves if you can as he'll get used to your scent and touch quicker. By next session he will probably have accepted being stroked on the back by a finger and not jerk round. So you can then move onto cupping a hand under him while he's walking around - just slide the palm of your hand under him but let him walk off. Then try sliding the palm of your hand under him and lifting it about 1cm but still let him walk off. Once you can do that fairly often, you should be able to pick him up easily - but take it slowly - so cup your hand round and let him walk from hand to hand like a tunnel at first - just for a few seconds - I find they get a bit annoyed with that after a few seconds. He should then be hand tame - used to your scent, and trust your touch.
Even then, when they're young and quite fast (and he will be fast out of the cage!) they often don't like being held for long and picked up much but they get better as they get older. But it's important to keep up reglar contact and out of cage time so they don't slip back into being too independent.
If you have a playpen rigged up it can be good to get him out in that every 3 days or so and sit in it with him - still with a few toys in the playpen. They run over you as if you're an object and he'll soon get used to you then. Be careful to keep away from the sides or they can try and use you as a ramp to get out!.
In the bathtub he will probably just slither up and down the sides at first trying to get out - which is a good time to try a stroke on the back. But eventually he may explore any toys or tunnels you've put in the bathtub. If you've used the ball - leave it in there. Ours used to hop back in it when he'd had enough and wanted to go back to his cage.
Even in a large playpen area they will spend most of the time trying to work out how to get out. If he starts digging at the corners after 15 minutes or so he's probably had enough so put him back in the cage. Hiding the odd treat in the toys in the playpen distracts them and they spend time foraging for them.
Cage:
I think he will feel more secure in the cage and come out more if he has a large house. They will ignore a small house because they like to have somewhere dark to retreat to which is why he's burrowed down. But I've found they are scared of coming out when it's open above. With a large house he will feel more secure. A tank can also feel a bit open and exposed above so a large tube or tunnel would help him feel more secure.
So what I would do is make a shoe box house (cardboard is light and will sit on tp of the deep substrate) and pop it over hiscurrent nesting area in the corner. Maybe pushed down a bit so the base is part under the substrae. Cut the base out of a shoebox and keep the lid as a lift off roof - so you can check inside without having to take the house out. Cut a hole for a door near one end of one of the long sides as an entrance and put a bendy stick bridge tunnel over the entrance door. This will mimic a burrow and be nice and dark inside. The bendy bridge also makes a ramp up to the flat roof. If the shoe box is large enough you could put a litter tray inside it - at the door end (they tend to nest furthest away from the door where it's darker so the litter tray is usually used at the other end).
I've found when you give them a large house, they move their pee corner inside the house and have an ensuite bathroom - so putting a corner litter tray inside should work well.
He will then feel more confident being out and about in the cage as he has a large comfortable house that's dark inside. Puta big pile of torn up strips of plain white toilet paper near the house (but not in it) and he'll probably build a nest in the house with it and can still burrow down in the substrate and bury his hoards under the house.
This has always worked best for me. I did try deeper substrate and no house with our last syrian and his ears were always down when he emerged from under the substrate - the burrow kept collapsing and was a permanent stinky mess! He was much happier with a house that mimicked a burrow.
If you can get one of those large cork log tunnels (reptile stores sell them) for the centre of the cage, that will also help him feel less exposed from above - a big dark tnnel to go from one end of the cage to the other (it could straddle the divider) and also something to climb over with an interesting texture.
I think the divider could be a bit lower so it's not such a drop to the other side so smaler bendy bridges might be better. Either that or raise the wheel as far as it will go on it's stand and have more substrate in the wheel side - so it's less of a drop and the cage isn't quite so segmented.
More floor toys generally to fill the space and hidey places - will also help him feel more secure. Things like coconut huts and cardboard tubes etc.
Mojito: Progress/Advice
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