You may not feel like having another hamster straight away, but we now have another one and it brought us all so much joy and laughter having a new baby hamster in the house. Until we got another one we were all a bit down. I desperately wanted another one within a couple of weeks - not to replace our Syrian, because he was himself, but I really missed having a hamster to care for, and the rewards it brings, and had a bit of an empty hole. Kept seeing hamsters but wasn't quite ready. In the end I waited a bit longer because Souffle kindly offered us one of her next litter. But there is no right time to wait. Some people get another one straight away, some people wait a bit. It helps to get another hamster that is a bit different - a different sex or colour. So they are "their own person/hamster" kind of thing and they also have different personalities
Newt, our current Syrian is much more outgoing and active than our previous home-bod snuggly boy! Just different.
I did find, after a fairly traumatic end to our Syrian boy, that it helped me having another hamster, and being determined to get everything right next time around. They are very forgiving when you don't always get things quite right though.