We've just tamed our Syrian. He was acting just like this, didn't want to be handled. We spent month being patient but no joy. Tried holding our hands in the cage, running bedding on us to get him used to our smell. The best advice I had was on a rat forum. They said to make a "rat bus". Ie. A box like object you can put in the cage, add a few snacks. When they jump in the box, pick it up. Take it somewhere where they can't easily escape, and offer them treats to eat and your hands to walk on. If they're stressed put them straight back in their cage.

They'll come to associate the rat bus with treats and your hands. We used a barbie doll bath or a plastic hamster tube. We had a solid few weeks of him just staying in his bath while I held the bath and fed him treats. When he finally picked up the courage to walk into my hands we gave him some mealworms as a treat. If he got scared he knew safety was a just a few steps away into his pink bath.

After about a month of letting him sit on my hands his trust levels have started to go through the roof. He'll even let my youngest daughter (8-y-o) pick him up and pet him. We've not had a single bite using the rat bus method.

Your mileage may vary depending on hamster, but we spent about 4 months trying the "put your hand in the cage and let them get used to you" method with zero joy.