“One person who has recently been diagnosed has been in contact with you,” the script told her to say. “Do you have a few minutes to discuss what that exposure might mean for you?” Forty-five minutes later, Ms. Cross hung up the phone. They had giggled and commiserated. Her file was crammed with information.

She was taking her first steps up a Mount Everest of cases.

Massachusetts is the first state to invest in an ambitious contact-tracing program, budgeting $44 million to hire 1,000 people like Ms. Cross. The program represents a bet on the part of Gov. Charlie Baker that the state will be able to identify pockets of infection as they emerge, and prevent infected people from spreading the virus further.

This could help Massachusetts in the coming weeks and months, as it seeks to relax strict social distancing measures and reopen its economy.