Can you look for a stolen Uzi with serial number SA68207?

If it's not reported stolen, you need to do that immediately. If it's taken into custody by law enforcement, the serial numbers will be run. If it's taken into possession by an FFL licensed firearms dealer, they're also required to run the numbers, and it will come back to them if it's stolen. Once the NICS system receives a report of a confirmed stolen firearm, police will be dispatched immediately to retrieve the weapon, and arrest the person who was in possession of it. At some point, you will be notified. If the weapon is able to be returned to you, you will be contacted with instructions as to how to go about doing this.

So long as it is reported stolen, there really isn't much else you can do.