TORONTO—About a day after Chinese researchers published genetic information on the new coronavirus in mid-January, a Toronto laboratory ran its first diagnostic test on a suspected case. The result was negative.

By early March, Canada, with a population the size of California, had completed close to 3,000 coronavirus tests. The Centers for Disease Control and Prevention, meanwhile, had run less than 500. Although U.S. testing expanded last week, local officials have complained that they still can’t keep up with surging demand....