Oof, definitely a risk with having liability only. I often maintain full coverage on most of my vehicles even after they're paid off because of things like this. But perhaps in your specific situation that doesn't make sense.

So a tort claim will be your real recourse. I would recommend getting a police report (just call it in, get a report number), get everything repaired after getting several documented estimates, get photos ASAP of the area (hope it's still in the state it was when the incident happened), the car, and a statement from any witnesses, and file a claim with the DC Tort Claims office. Keep in mind you usually need to have paid for the repair and have a receipt, and they try to procedurally drop claims, so have all supporting documentation.