DC/VA car purchase question

Hello all - looking for advice on buying a car. The current owner lives in Virginia and we are buying it from her on Monday. We live in DC but have Virginia drivers licenses. We plan to get DC ones soon but we need to buy the car Monday, and can’t get licenses by then. We aren’t allowed to register a car in DC without a DC license. The owner will need to return the Virginia plates once she sells it to us. Can we temporarily register the car in Virginia until we get our DC licenses and register it there? Or, if that’s not possible, what can we do? Thanks in advance!