Generally, if your appointment is in the morning, they might be able to do same day oath. For my wife, after her interview, she was asked to wait in the seating area with a lot of glass windows. She was then called at the counter and was given the oath letter. So my recommendation would be dont simply leave the building. See if you can get called at the counter if same day oath doesn’t happen for you. Let us know how all of this went. Mine too is in mid-January.