Hi. I'm really sorry to hear this. If a small baby dwarf hamster has escaped, it is likely to be frightened and hiding somewhere. I think cats tend to not eat them, but as with other prey, they can "play" with them or injure them. So providing you can't see that the cat has done that or brought you anything, then hopefully your hamster hasn't been found by the cat.
The tricky bit now is finding and catching the hamster, while making sure that cat doesn't. The best option for catching a hamster is a bucket trap - I'll link some info about how to set one up. So tonight, before bed, if you set that up in the same room the hamster cage is in, and leave the doors open to other rooms (in case the hamster is no longer in that room), but you'll need to keep the cat shut in your bedroom with you!
Do you have two floors (eg a house?). If so, the hamster is most likely to be downstairs, so could you manage to keep the cat upstairs in a bedroom with you overnight?
If you're pretty sure the hamster is still in the same room as the cage (eg if you've heard any noises or seen signs of it) then instead, close the doors to that room when you set the bucket trap.
Meanwhile, keep a close eye on your cat - could it go outside for a while? Or is it an indoor cat? If it doesn't go outside, then see if you can keep it to one room for now (a different room from the hamster cage).
You could try listening carefully to see if you hear any noises, but the chances are, it will be asleep somewhere if it's daytime - at least until about 8pm at night (if you're in the US it may not be that late yet

). And even then it may not venture out until after dark.
If it ventures out after dark, then it will be looking for food and foraging materials. Hence you leave a trail of food up to the bucket trap (just the occasional treat spaced out leading to the bucket trap). Eg sunflower seeds. Near the top, have smelly treats to attract the hamster - cucumber, cheese or strawberry eg.
I really hope you find hammy - and if you need any help, just keep posting. Just a tip also, it's better not to keep two dwarf hamsters in the same cage as they can also fight and kill each other! Even though some pet stores still sell them in pairs.
If you have a spare cage you could move the remaining hamster into that - with bedding and set up etc, and put the current cage on the floor in the room with a ramp leading up into it (as well as the bucket trap) as they often want to go back to their nest and familiar smelling environment.
Photo and description of bucket trap here
The best way to catch an escaped hamster is to use the bucket trap. Information on how to set up a bucket trap and other methods to catch your hamster are in this article. It's also important to make sure your hamster cage is secure and...
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