If social distancing can bring the number of cases down to a manageable level, you can switch to a traditional public health approach: Test anyone showing symptoms, and aggressively trace and test any contacts of known cases.
If you can identify the remaining cases and isolate them, you're fine. The danger is that some cases slip through the contact tracing procedure (e.g. the identified patient forgot about someone they were in contact with) which is why you also want to aggressively test anyone presenting with symptoms.
