Now obviously there are scaling issues going from 3300 people to millions but I'm not sure it's impossible. S Korea also mostly controlled things by testing.
Training the postal service to be able to take nasal swabs could scale this though you would need to robocall all those on the postal route what time to present themselves at the edge of their property. Starting with geographic locations where there have been clusters, then individual cases, then the general population. Also when an antibody test is available have them delivered by the postal service with instructions and URL for a video on how to administer it.
Now obviously there are scaling issues going from 3300 people to millions but I'm not sure it's impossible. S Korea also mostly controlled things by testing.