Start by shrinking the world he can hide in
A loose Syrian hamster is rarely far away. Syrians are solitary, nocturnal, and drawn to narrow dark gaps, so yours has most likely wedged himself behind the cage stand, inside a sofa base, or along a skirting board in the same room. Close that room's door, push a towel along the bottom gap, and keep cats, dogs, and children out. Work quietly, because loud searching and furniture dragged across the floor will drive a frightened hamster deeper into cover rather than out of it.
Check in a deliberate order: behind and inside the enclosure stand, under low furniture, inside shoes and storage boxes, behind books, and in any warm spot near a radiator or appliance motor. Use a torch at floor level and look for droppings, hoarded seeds, or chewed material, which tell you he has passed that way even when you cannot see him.
Make his own cage the trap
Do not chase a hamster you spot, and do not grab at one half-hidden in a gap. Instead, place his enclosure on the floor with the door open and a ramp or low step up to it. Put familiar bedding that already smells like him inside, plus a tiny piece of cucumber or cooked egg as a lure, and his water bottle where he can reach it. A Syrian returning to a known scent and a known sleeping place is far more reliable than a hand reaching toward him.
Count out a small number of sunflower seeds on the floor near likely hiding places before you leave the room. If seeds vanish overnight, you have narrowed the hiding place without seeing him, and you can focus the cage trap in that corner the next evening.
Search the night shift, not just the day
Syrians wake as the house quiets. If the daytime search finds nothing, sit still in the darkened room in the evening with the lights low and listen for rustling, scratching, or food being pouched. A flour dusting across a doorway or in front of a suspected gap can show tiny footprints by morning and confirm which side of the room he is using.
Check washing machines, tumble dryers, and recliner mechanisms before anyone uses them, and look inside them only with the power off. Lift nothing heavy alone if he might be underneath it, because a shifting bookcase or sofa can injure a hamster pressed against the floor. Move one item, look fully, then move the next.
Once he is back, fix the exact exit
When you catch him, by hand only when he walks onto you willingly or steps into a mug or tube you can cover, return him to the enclosure, offer water, and watch that he moves normally and has no cuts or limping. Then find the escape route before the next night: a lid that flexed, a bar gap near a corner, a door catch he learned to lift, or a chew hole in a plastic base. Weight or clip a loose lid, replace chewed panels, and keep the cage away from climbable furniture that shortens the drop to the floor.
If he is still missing after the first night, or you find him injured, breathing fast, or unable to walk straight, call a veterinarian for advice rather than waiting for another evening search. To widen help beyond your own rooms without panic, KinsLe's Lost Pet Alert System lets you alert nearby members that a Syrian hamster is loose nearby, so neighbours check garages and hallways carefully instead of assuming every rustle is a mouse.