That must have been a shock for you and Ginger
I would wait a little then try and spoon the pups in to the nest as they will not last long without mother's attentions I'm afraid. It is something that does happen so don't fret if she does not accept them back and you did your best with not touching them etc. She may also detect there is something wrong with them and this is why she is leaving them. If they are still wiggly then get them as near as you can to her. Birth usually takes around two hours so she may well gather them up soon.
Wire levels are really unsuitable for hamsters so a new cage is going to be required or lining this one with cardboard or lino but only when the pups are out with eyes open.
For now keep her very quiet and nobody should peek or bother her.
Feed some baby food or porridge and put it on the far side of the cage from the house. When she is out try and spoon the pups in to the nest. The house will soon be two small so give her masses of ripped loo roll to hopefully make an outside nest in. With any luck she will move them in the night.
Prepare yourself to accept whatever mother decides. She may raise all or some or may cull them all. It is hard when she is not tame or used to her new home really but don't worry as you are not the first nor will be the last. You can only try and make everything as quiet and peaceful for her as you can and cross your fingers.
Good luck and keep asking. We will guide you through.