It's just time and patience xxx It's very hard when a child wants to hold him but it's worth it when you get there. I assume he's a baby and they can get scared easily. Some noise may have freaked him or he may have just been having one of those days where he was feeling a bit overwhelmed with it all. It sounds like he isn't hand tame yet if you can't pick him up.
Maybe give him a couple of days left alone and just talk to him through his cage so he gets used to your voices. We've had two Syrians now. The first one was from a pet shop and completely untame. The first mistake we made was his cage was too small and he got stressed and a bit aggressive and wanted to be out all the time chewing bars. We moved him to a better cage and that freaked him out. He was settled within 2 weeks though but it set taming back so we had to start all over again. We did bathtub taming. Similar to a playpen area but in some ways maybe a bit easier for taming as less space?
We couldn't even touch him without him jerking around as if threatening to bite, but had him out in the bathtub 2 or 3 times a week (dry with plug in!) and a few toys and he just slithered up and down the sides mostly. At these times we would stroke him on the back with one finger. Once or twice during the session and eventually he stopped jerking round and accepted being stroked on the back by finger. After that we moved onto cupping a hand under him as he was walking around and lifting it slightly - just 1cm or so - and not trying to hold him but just let him walk off. We did that a few times and then we could pick him up and hold him and he was tame as anything! Even then they may not like being held for long or want to sit still but you can then have them out on the sofa exploring and interacting with you (I'd put a blanket over it though so he can't get down the back behind the cushions!
With our current Syrian, he was from a breeder and already hand tamed. But once we got him home he got scared and skitty - I had him out in a playpen area that was quite large and he was so fast that handling was difficult so it took a bit of time before he settled to being picked up and relaxed too. But he's now tame as anything.
They just need to learn to trust you and be familiar with you. Does he want to come out of the cage at night or do you have to tempt him out or lift him out?
When they aren't hand tame, if you do pick them up they can "ping" - ie wriggle out of your hands and leap 2 feet in the air so best to try it low down and over some cushions. But if he's not liking attempts to hold him then step back a bit and take it slowly.
It's very hard! I also thought our first Syrian would never be tame - but when it happened it was instant! Suddenly he trusted us and was happy to be handled, popped in my dressing gown pocket on the sofa and would even go to sleep on your knee if he was dopey.
They all have different personalities as well - some are quite lazy and others maverick and never sit still. I think different times of the evening are different too, depending on the hamster. They can be very fast and active early evening and late at night, but often in nap mode and a bit more dopey around 8pm ish.
The other thing that can affect them and make them jumpy is cage cleaning or changing things in the cage. It's not necessary to clean them out weekly as pet shops usually recommend and best not to clean everything at the same time so something always smells familiar to them. Generally it's recommended to leave them two weeks without any cleaning so they settle in and not disturb things or move them round in the cage. And even then you can just "spot clean" the toilet area. Taking a handful of soiled substrate out, adding a new handful and just mixing it in a bit. Using a litter tray means the cage mostly stays clean anyway and you empty the litter tray every 5 days or so. They are quite clean little things really and like to organise their house, nest and hoards. They can get quite upset if you take their nest or dry food hoard away so I always leave those unless they're pee'd on. If you have to remove them, then put a bit back that is dry even if a bit whiffy - in exactly the same place and add new food to replace the hoard in exactly the same place and a pile of new nesting material in the cage so he can rebuild it (torn up strips of plain white toilet paper is safest and they can pouch it and take it to the nest).
The more substrate you have, the less often it needs cleaning out as the bottom half tends to stay clean and dry. I use a litter tray with chinchilla sand in and only do a substrate clean about every 3 months. I do the wheel occasionally, as and when, or give any toys or other contents a wipe or wash as and when but not all at the same time.
This litter tray is a good size for Syrians and fits in a corner (they often choose a corner of the cage as their pee place). If you put it where he pees with some chinchilla sand in, and a tiny bit of his pee'd on substrate on top he will probably start using it straight away. But if you put it somewhere else he'll ignore it!
Adding something like a litter tray or additional toy at this stage is fine but important not to take anything out he's got used to (unless it's a safety issue) or move things around.
They scent mark their cage when they move in via glands on their sides and underneath, which creates a trail they can follow so they can find their way around and know where everything is as they don't see well at all. If all their scent is removed they are lost. As they get older they accept cage cleans better but still best to do partial cleans really.
It may be he isn't full settled in his cage yet and wants to feel secure there before you can progress with taming.
I would start again. Give him 2 or 3 days left alone in his cage and keep talking to him in a gentle voice through the bars. Unless he is showing he wants to come out then fine, let him out for a taming session. You can also do the tissue trick where you put some sheets of toilet paper up your sleeve against your skin for a few hours then tear them into strips and add them to the cage - he will take some for nesting (the pile goes down slowly but he will take some) and it will help him get used to yours and your daughters scent (maybe your daughter do the tissue trick?).
Then offer him treats through the bars for a few days and then moving on to taming out of the cage again. Best not to put your hand in his cage too much as that can freak them (invaders!) so if he isn't coming to the door to come out you can use a tube with a treat in one end. Put the tube in the cage andwhen he goes in it to get the treat, lift it out with a hand over either end. If you have a hamster ball I would have that next to the cage and then put one end of the tube in the ball so he walks into the ball and pop the lid on. You can then safely carry him to wherever you're going to do taming (eg the bathtub). If a ball fits in the cage you can put that in the cage with a treat in so he hops in.
Pumpkin seeds can be popular as treats but if you want to tempt him into something then something nice and smelly like cucumber or a little bit of cheese works well.
I've added a little video of how we tamed our last Syrian. It doesn't show much but has the tips mentioned above. You will get there! I know 10 year olds can get bored quickly but they also have good ideas. She may lose interest when it doesn't happen quickly but when you get there she will be able to have a lot of interaction with Scout - they come back to interests too.
My stepson was 6 when we got our last hamster and it was so hard because he just wanted to pick him up and cuddle him but he did enjoy the taming sessions and videoing them!
This is the litter tray
https://www.amazon.co.uk/Hamster-cor...=hamster+potty
And Chinchilla bathing sand - I empty it and clean it out every 5 days or so - the sand soaks up the pee. They tend to neatly pee in the very back corner (where it's higher so it doesn't spray) and sit in the front for a little wash
I get two boxes at a time to save on postage but one lasts for ages.
https://www.viovet.co.uk/Supreme-Sci...q=sand&sct_r=1