Daniel Hom, 77, a pharmacist who lives in Berkeley, Calif., and works in nursing homes, said he filled out the survey on Sunday night around 8 p.m. and found out that he qualified for the test. He said he thought his age was the primary factor for becoming eligible, because his son, who is in his 30s and also works in health care, was not selected.

On Monday morning, Mr. Hom said he drove to the parking lot of the San Mateo County event center where he got a nasal swab. “They stuck it way up there,” he said. Mr. Hom was told that results should arrive within four days by email depending on how quickly Quest Diagnostics can process the test.

“I was impressed how organized they were, considering it was the first day,” he said.

Verily said it was trying to help public health officials expand access to testing in areas with a high volume of known cases. The new site is supposed to direct so-called high-risk individuals to newly opened testing centers in Santa Clara and San Mateo Counties, which include Silicon Valley.

The first issue appeared to be a result of what the site was intended to do. It started with an initial survey asking whether people were “currently experiencing severe cough, shortness of breath, fever or other concerning symptoms.” If they selected “yes,” the site abruptly ended the survey and said in-person testing through the program “is not the right fit.” In smaller font, Verily suggested seeking medical help.

Responding “no” to the symptoms led to more questions to gauge eligibility for testing by asking age, location and other factors. This caused confusion among people trying to use the site.