It's definitely baby steps with taming
I used the Rosewood little hearts as taming treats - you could also use pumpkin seeds for a bit of variety (you can get a small bag of those on the bakery counter in supermarkets).
The main thing is to try not to go too quickly, which is hard when you have a new hammy! The first 2 or 3 days they need to be left alone mostly to settle into the cage and scent mark and start feeling at home in the new environment. After that generally it's recommended to start feeding the odd treat through the bars and talking gently so they get used to your voice, then move onto having a treat on the palm of your hand and see if they walk onto your hand. But - a hand in the cage can freak them out! So if you could do that bit with your hand near the entrance door to the cage and let them come to you that's better.
You can also do the tissue trick which helps them feel familiar and positive about your scent. Put some sheets of plain white toilet paper up your sleeve for a couple of hours (or down your bra) then tear each sheet lengthwise into 5 or 6 strips and put a pile of the torn up toilet paper in the cage somewhere. Your hammy will gradually pouch them to take to his nest to build it up. You might not see this but the pile should go down gradually - so then they have your scent in their nest.
The main thing is that the first two weeks settling in are really important to future progress - so don't clean anything or move things around for the first two weeks. You could add the odd new item if needed. And you can spot clean the wee area every 4 or 5 days (or longer even) just doing it if and when it gets a bit whiffy - ie take a handful of substrate out and put a handful of clean in, and mix it in a bit so it still smells familiar. Always try and leave their nest in tact - at least for the first two weeks. After that, if he has pee'd in his nest and you have to remove it, then leave as much of the old nest behind as you can - the dry parts - they get very upset about having their nest stolen! The same with hoards - don't remove them unless wee'd on and if you have to remove some then put new food back in the same place to replace it (obviously eventually some of the hoard will need removing if it gets too big, during a cage clean, but not too often, plus you need to check there's no fresh food sitting there to go off now and then - I find any fresh food gets eaten straight away rather than hoarded).
My biggest tip to avoid lots of cage cleaning and stress, is to use a hamster potty/litter tray - they tend to just start using it, if you put it in the corner they've chosen as a toilet. Then you just empty the litter tray every 4 or 5 days, wipe it out, refill it, and the substrate stays clean and dry. Our hamster only wees in his potty and very occasionally in his wheel - he's a clean tidy little boy!
Have also added a link to Erin's Hamsters cage cleaning tips video which is full of excellent advice about what kind of method to use to avoid stress to the hamster which can set back taming and just be bad for them generally.
Your new little hammy sounds lovely. Ours was quite slow to hand tame, but your sounds like he is doing well. They are often less territorial about hands when they're out of the cage - in the cage is their territory - so a safe place to put them out of the cage to get used to a bit of handling is a good idea - some people use the dry bathtub with the plug in (with a towel on the bottom and the odd toy to hide in or for interest). They can run around safely in there and not hurt themselves if they jump when you try and touch them. We did the bathtub taming a couple of times a week - so have also added my little video on that - it's not great quality and doesn't show much - but has some tips on how to progress
Most of the tips I learned on here.
https://www.youtube.com/watch?v=5jVnEjrXbww
https://www.youtube.com/watch?v=kjyEme2xcq4