Get a bucket, fill a few inches with shredded newspaper. Put a few hamper treats in the bucket. Get a length of wood, something wide enough for the hamster to walk along, & long enough that it could make a 'walkway' from the floor to the lip of the bucket. Fix it on so it doesn't fall in the night & cause a hamster tragedy. Put one or two hamster treats on the walkway. Leave.
Hopefully, in the morning, the hamster will have walked up the walkway, fallen into the bucket, & be safe.
Can't make any promises but this worked for my Dsis.
Get down on your hands and knees and examine the floors for tiny poops. When ours escaped, he had made a nest (with Barbie clothes and board game pieces) behind a bookshelf...two floors away from his cage. I found him by following a trail of poop he'd left on the carpet.
I'd go round all the edges at floor level, systematically in each room. The hamster is probably asleep somewhere if its morning, so listening out for it won't be so helpful.
Check in dark places - behind wardrobes.
I lost our hamster for about 2 hours - in the end I gave up looking and started MNing because I couldn't go to sleep (it was after midnight by then) and then spotted the hamster coming down the stairs in the corner of my eye! But at least it was night-time - definitely hamster-moving-around-time.
If you don't spot it in the day - at least you have a chance once it is moving around in the evening again.
Yay! I'm so pleased you found it! What a relief, I hope your boys are pleased?
I guess there are two options how it got out:
1. human error - though not admitting to it, one of your DSs left its cage-door open or forgot to put the hamster back etc. In which case, it won't happen again after this scare!
2. there's something wrong with the cage. Check whether the cage door (s) is loose at all - could the hamster push it open? Tie it shut with something that won't hurt the hamster if it nibbles on it!! And tell the teacher on Monday if the cage is not working.