Within an hour after Hayward Fire Station 7 began offering free coronavirus testing at 9 a.m. Monday morning — one of the first free testing sites in California with no doctor’s order required — firefighters had screened nearly 300 people for symptoms, collected nasal cavity samples from about 20 of them and prepared to drive the samples across the bay to a lab.

By 11 a.m., technicians and clinical laboratory specialists at Avellino Lab, the Menlo Park biotech company that is providing and processing the tests, was running samples through its diagnostic machines. Results were expected within nine hours — far faster than the several days many physicians’ offices are waiting for results for their patients.

The Hayward testing facility is believed to be one of the first of its kind in California, in which a local fire department is working with a local biotech company to provide and expedite free coronavirus testing with same-day or next-day results. If successful and scaled up, it could help relieve pent-up demand to get testing and results quickly, which would help infectious disease experts understand how widespread the coronavirus is becoming.

“The Hayward Fire Department and municipal team at the city did an amazing job to say, ‘We’re not going to wait. We’re just going to go forward with this and do our best,’” said Eric Bernabei, a spokesman for Avellino, which is suspending its regular work in rare diseases and eye conditions to focus on coronavirus testing. Avellino plans to provide enough tests for the city of Hayward to conduct 350 tests a day, seven days a week.

Also on Monday, Verily, the life sciences arm of Google, announced it will expand Project Baseline, an initiative it launched March 15 to screen potential patients with COVID-19, the disease caused by the virus, online and direct them to testing sites in San Mateo and Santa Clara counties. The project will be launched as well in Sacramento County and Lake Elsinore (Riverside County). The tests are free, but it takes several days to receive results. Verily said in a blog post Monday that the initiative has tested about 1,200 people.

The testing partnerships speak to the urgent need to get more Americans tested, and fast. For weeks, doctors have expressed frustration that they simply do not have enough tests for all their patients who they feel should be tested. Even though diagnostics companies are coming out with their own tests piecemeal, they have yet to make a significant dent in the worldwide shortage of tests and test components like swabs and vials.

“I don’t know where those tests are going,” said Dr. Charles K. Morris, a primary care physician in San Francisco who estimates he’s seen about 20 patients recently that he wanted to order a test for, but couldn’t because he didn’t have enough tests. “They’re not getting them to us, or at least not here.”

And for the patients Morris was able to test, he has had to wait three or four days — and in one case, 10 days — to get results back from the lab company that is processing them.

“It is nearly impossible to obtain swabs and viral testing vials,” he said. “We are still so far behind the rest of the world in this, it is shameful. We cannot get ahead of a virus that is doubling in spread and deaths every four to five days when we only have enough kits to test the already sick but not their contacts, and the turnaround is three to five days.”

A number of Bay Area providers have started testing in drive-through and clinical settings, but demand is so high that they are not able to test everyone quickly, even those who are showing symptoms and who meet many of the criteria. As a result, many residents desperate to get themselves or their high-risk family members tested are getting the runaround.

Sophia Nguyen of San Jose, who began experiencing a fever and dry cough around March 13, spent several frantic days trying to obtain a test for herself and her diabetic mother, whom she lives with and who also began showing symptoms a couple of days later. Her mother’s primary care doctor told her they didn’t meet the requirements to get tested and to call the local hospital. The hospital, after putting her on hold for three hours, referred her to the website of the U.S. Centers for Disease Control and Prevention, she said.

“It was just a circle of confusion and people telling me to go to different places, with no solid answers,” said Nguyen, who was particularly concerned that her mother’s blood sugar began skyrocketing. “It felt like life or death.”

So Nguyen tried Stanford, but the process of going through the initial screening and then lining up a telemedicine visit with a doctor took four days, she said. In the meantime, she tried Verily, and was told she qualified for testing but that it would take a few days for someone to get back to her.

Finally, with the help of friends scouring the internet for information about testing, she and her mom reached out to Carbon Health, a San Francisco health care startup that offers primary and urgent care. They did the online diagnostic test and got tested the next day at a clinic in Cupertino. They submitted samples on March 17, and were told their results would come back by Wednesday, eight days later. Nguyen said both she and her mother are feeling a bit better, but her mother is still having some shortness of breath.

Faster test results, which the Hayward testing site is aiming for, could help cut down on confusion and wait time for people like Nguyen and her mother. If scaled up quickly, it could also help public health authorities get a better handle on the virus. South Korea, the country that has thus far appeared most successful in “flattening the curve” to slow the spread of the disease, did so with the help of aggressive and widespread testing early on.

The Hayward site, as is the case with most testing facilities, is prioritizing first responders, health care workers who come into frequent contact with people who may have the virus, and the sickest and highest-risk patients — those who are older, have underlying medical conditions like diabetes and hypertension, or who may have had direct contact with a known COVID-19 patient. Potential patients do not need to get a referral from a doctor, but do have to go through a screening process with seven different criteria before they’re asked to park their cars and take a swab test. Those criteria include having symptoms such as shortness of breath, a fever or a cough, and a recent history of traveling abroad.

Sixteen firefighters are assigned to the Hayward site for the next seven days. After seven days, they will be tested and swabbed, and given two days off to see if they develop symptoms, and then will return to duty. When they finish their seven-day shifts, another rotation of 16 firefighters will staff the testing site, Hayward Fire Chief Garrett Contreras said at an Alameda County Board of Supervisors meeting Monday.

“All of the testing will take place in a tent, whether it’s raining or not,” Contreras said. “We are managing this like a significant wildland fire, and that is the reason for the seven-day commitments.”

A separate line and isolation location exists for homeless people. If someone is tested, they will be presumed positive, Contreras said.

The testing facility, which is expected to be operational for at least three weeks, cost $500,000, and Contreras said he plans to transfer an additional $500,000 for the effort. Contreras said he plans to meet with county officials this week to analyze the launch and see if it can be rolled out to other locations in the county.

Catherine Ho and Sarah Ravani are are San Francisco Chronicle staff writers. Email: cho@sfchronicle.com, sravani@sfchronicle.com Twitter: @Cat_Ho @SarRavani