Also - if and when you move him, this needs to be done carefully. Assuming his current cage is not teeny tiny, then it's best to leave him to settle into that for at least two weeks before moving him now. Coming home with you is a big change of environment and a stressful time for them. It taks a good two weeks for them to adjust, scent mark their cage. Too much stress in the early days can lead to illness.
So general advice is - leave them alone for the first couple of days and just put food and water out. After that, don't clean anythng or start making lots of changes in the cage for two weeks. You can just spot clean the pee area every few days. ie take out ahandful of wet substrate and put a handful of new in, then mix it in a bit so it smells familiar. Adding the odd new thing is ok, as long as it doesn't mean moving things around, but taking things out upsets them. So only do that if it's an urgent safety issue!
Best thing is to add a litter tray with Chinchilla bathing sand in it (must be sand not dust). You put that in the area they have chosen to pee with a tiny bit of the pee'd on substrate on top and they use it. Then you only need to empty the litter tray every few days and the rest of the cage stays clean.
So apart from the spot clean/litter tray don't clean anything for two weeks to give the hammy that adjustment time and to scent mark their way around the cage.
Even after that it is best not to overclean or do "full" cleans. And it doesn't need to be done weekly. ie don't clean everything all at the same time, or it removes all their familiar scent and they get very stressed and want to escape - and can start chewing their way out. They either feel in a strange place or feel they've been invaded.
So to avoid that, when you do finally do a substrate change (it can go 6 to 8 weeks with a litter tray and/or spot cleaning), don't clean anything else at the same time. So you can do the wheel a different week,and any toys as and when needed. Toys often don't need cleaning that often. Also save a bit of the clean old substrate and sprinkle it on top of the new so it smells familiar.
If they don't pee in the nest it is best to leave that alone - they are very precious about their nest and hoards. I have a house/nesting box with a lift off roof - so I can check inside and don't need to remove the house - so the nest doesn't fall apart.
If the nest or hoard is pee'd on then you need to remove it, but try and leave a bit of the old nest behind, that's dry so it smells familiar and hasn't completely gone. Then just put a big pile of strips of plain white toilet paper in the cage (but not inside the house) and the hammy will pouch some, take it to the house and rebuild the nest.
Same with the hoard. If it's not pee'd on, then leave it. Next time you do a substrate change, if it has got very large, you can "prune it" down a bit but add a bit of new food as well. If it's been pee'd on and has to be removed then always replace it with new food in exactly the same place. Otherwise they start having abnormal behaviours and will pee on everything to deter people from stealing it! Then it becomes a catch 22. So I show great respect for my hammy's nest and hoard - it's his bed! And his kitchen and they are very particular about it.
If they're dry they can go quite a long time. My hammy just keeps adding to his nest and chucking bits out and refurbishes it himself.
When cleaing the cage base, avoided strongly scented cleaning things. Unless there has been illness or disease, it doesn't need disinfecting - just warm soapy water will do and then rinsed well to remove any scent. Their sense of smell is much more powerful than ours and scents can affect their breathing.
Anyway - so give him 2 or 3 weeks to settle in to the current cage. Then when you move him over it's a good idea not to do it cold turkey. The day before, let him play in the new cage. Put new substrate in and a couple of toys (eg cardboard tube) and maybe one toy from his old cage. He may freak out and want to come out very quickly. If he does that, put him back in his old cage and then let him play in the new cage either later that evening again or next day. Second time he should be more interested in exploring.
Then the day after - put him somewhere safe and move everythig over. You can leave all the new substrate in the new cage, but also move all the old substrate over from the old cage and spread it on top - this helps settle them in quicker.
Also try and set it up so things are in the same layout as the old cage, or as close as possible/similar.
Resist the temptation to clean everything when moving things over - because it really helps them adjust to the new cage quicker if everything smells familiar. Even then the hammy will be a bit jittery for a few days and will need another two weeks to fully settle. But during that time you can still do the odd bit of out of cage taming if he wants to come out. Best to avoid trying to do it in the cage as they are quite territorial in the cage.
Anyway this is the kind of litter tray I use - works well in the corner of a cage which is where they tend to choose as a toilet. If you put it in their chosen place they will use it. But if you put it anywhere else they will ignore it!
https://www.amazon.co.uk/Hamster-cor...gateway&sr=8-6
This one looks similar
https://www.amazon.com/Ware-Manufact...gateway&sr=8-9