I’m assuming LA has Congress people in DC who hire summer interns or semester interns. Of course, most of these kids are NOT going to college in DC. Your kid could apply for these summer internships which might involve work in DC, or might involve work at a congress person’s in state office(s).
I’m not sure why you think that it’s essential for this kid to attend a college that is in close proximity to DC in order to eventually work in…DC. There are lots of government employees who didn’t attend college in the greater DC metro area. Lots.