Japan didn’t need to hire large teams of contact tracers. They were already in place. Nurses at their public health centers routinely contact community residents to provide health education and services (check on newborns, advise the elderly). https://www.bloomberg.com/news/articles/2020-06-23/the-low-tech-way-that-japan-managed-to-tackle-the-virus-quickly
Those established relationships with community members have been crucial because contact tracing involves sharing private information. These teams benefited from extensive on-the-job experience. It is not enough to hire someone. They have to know how to have a conversation.
These public health centers trace their roots back to tuberculosis control, and this continues to be one of their important functions. “For tuberculosis, you need to follow up for two years – the coronavirus tracing time period isn’t as long.”