That mix really isn't very good, it's too low in protein, certainly for a young hamster.
I would look for a better mix, if you can get Harry Hamster that's the best otherwise if you're in the US you may need to combine more than one mix.
You can also give things like a small piece of plain cooked chicken once or twice a week for a little extra protein, small pieces of nut or a monkey nut are good too in moderation along with a sunflower of pumpkin seed (both preferably in the shell) as healthy treats.
Begin slowly with veg, one tiny piece every few days to start with gradually building up to a small piece daily, as much variety as possible.
Here's my list of veg (ignore the bit about dwarf hams I'm just copying the list I always post!)
Safe veg, those marked * are relatively high in sugar so only feed to diabetes prone species as an occasional treat if at all.
Asparagus
Basil
Broccoli
Brussels sprouts
Common or red clover
Cabbage, green or red
Carrot*
Cauliflower
Celery
Chard
Coriander
Courgette
Cress (not mustard & cress as commonly sold together)
Cucumber
Dandelion leaves & flowers
Endive/chicory
Green beans/runner beans
Kale
Pak choi/Bok choi
Parsley
Peas/mange tout/sugar snap/snow*
Peppers, any colour
Potato/sweet potato cooked only*
Radicchio
Spinach
Squash/pumpkin*
Swede
Sweet corn/baby corn*
Turnip
You'll find some of the safe fruits
here I would stick to mostly veg rather than fruit though.