Experienced hamster owners recommend that it is OK to touch newborn hamsters 3 to 4 weeks after they are born.
The reason why you should not touch the newborn hamsters before 3 to 4 weeks into their birthday is simple: Scent.
Why you should not touch them before 3 to 4 weeks

• This is because mother hamsters identify their babies by their unique scent.
  When you touch them, you will leave a scent on them and their mom will not be able to recognize them and will not feed or take care of them.
  This will be fatal for the babies because the mother hamster may end up eating them or will leave them out of her nest and will not feed or keep them warm.
  

If you need to handle the hamster babies before they wean, use a pair of clean and non-abrasive gloves because baby hamsters have very sensitive skin.
Do this only if you have to because this will increase the risk of your baby hamsters being abandoned or eaten by their mother.
3 to 4 weeks is the time when newborn baby hamsters wean and it is only safe to touch them after that.
The reason why you should not touch the newborn hamsters before they wean is because you will take away the unique scent their mom recognize them by.
I hope you have learned something new from my article and I want to emphasize that you should touch your newborn hamsters, with a pair of gloves, only if you have to do so.
Wishing you and your hamster happiness!