SACRAMENTO (AP/KPIX) — As California began offering vaccinations to everyone age 16 and over Thursday, Gov. Gavin Newsom urged more residents to sign up for appointments and not let apprehension over inoculations get in the way of protecting themselves against the illness.

Nearly half of Californians eligible for vaccination have received at least one shot against the coronavirus, Newsom said as the country’s most populous state began vaccinating everyone, regardless of occupation or health condition.

READ MORE: Report: San Francisco Giants Lose Free Agent Pitching Ace Kevin Gausman To Blue Jays

Much of the San Francisco Bay Area had already opened vaccine eligibility to teenagers, with Contra Costa County extending eligibility to everyone who works or lives there over the age of 16 at the end of March.

Health officials in more counties have followed suit last week and this week, with Alameda, San Francisco, Santa Clara and Solano counties all making the age group eligible for the vaccination.

It comes as California and other states have seen vaccine supplies rise in recent weeks, despite the recent pause of the use of the Johnson & Johnson single-dose vaccine as U.S. government health advisers evaluate whether a handful of unusual blood clots were linked to the shot.

With the increased eligibility, that likely means many will have to have a little bit more patience as more people jump online for vaccine appointments. The milestone also raises the question of who might be getting left behind in the rush.

“As soon as we got on, there was kind of a crash of the website,” said South Bay resident Geoff Dear outside a vaccination site in San Jose. “A few minutes later, it opened up again. So it ended up pretty well.”

Dear is 25 years old and was able to get his first shot of the Pfizer vaccine Thursday. He said his friends aren’t far behind him.

“All the people I know, yes,” said Dear. “Especially my group. We’re trying to get in soon as possible. We want this to end as soon as possible.”

Newsom made a swing through vaccination sites in multiple counties, celebrating the full eligibility landmark, even though it will take weeks to make appointments available to everyone who wants one.

“I don’t care where you get it. I just want you to get it,” Newsom said of the vaccine at a news conference in Union City.

“We have to meet people where they are, and make it a lot easier, with no appointment necessary,” San Francisco Mayor London Breed joked at the opening of a new clinic. “Because I know my family. They do not take appointments. They say, ‘Where am I supposed to go?'”

“A large part of this is access,” said UCSF Epidemiologist George Rutherford. “We have data, from several studies now, which is the reason a lot of people are getting vaccines is because they can’t make the phone system work, they can’t get their appointments online.”

That, says Dr. Rutherford, is something a lot of people can actually help with.

“One thing people can do is help their neighbors,” Rutherford said. “Help their in-laws, help the relatives who are having a hard time accessing the system to get appointments and help that go and get vaccinated. That’s a big deal you can do to help right now today.”

California has seen coronavirus cases plummet from a deadly fall and winter surge. About 2,300 people are hospitalized with the virus, compared with nearly 10 times as many earlier in the year, Newsom said. The state’s seven-day positivity rate for new coronavirus cases is 1.7%.

California has administered 24 million doses of vaccine and is pushing residents to get the shot through community outreach, mobile clinics and public service announcements, including what Newsom said is a new $40 million Spanish-language campaign emphasizing that vaccines are safe and effective.

“We’re in the fourth quarter unquestionably. But this game’s not done yet,” Newsom said.

READ MORE: 'The Long Good-Bye'; New Hope In The Battle Against Alzheimer’s Disease

As vaccine supplies have risen, many residents have had an easier time getting the shot. Several counties previously opened up eligibility to people 16 years and older after seeing appointments go unfilled, and the rest of the state followed suit on Thursday.

Before opening up vaccinations to younger people, University of California, Davis Health had as many as 1,500 unfilled appointments a day. It is now booked for the week and continues to see strong demand for the shot, said Marianne Russ Sharp, a UC Davis Health spokeswoman. Sonoma County officials reported overwhelming demand swamped supply.

In San Bernardino County, which expanded eligibility last week, vaccine slots that used to be snapped up in minutes now might take days to fill, but they don’t go unused.

“The county has seen that it takes longer to fill appointments than in the past,” said David Wert, a county spokesman. “But they all get filled.”

That isn’t the case in nearby Riverside County, where county health officials said as many as 900 vaccine appointments go unfilled each day. The county of 2.5 million people has seen a jump in vaccinations of younger people since expanding eligibility, but it still has more doses than demand, said Michael Osur, assistant director of Riverside County Public Health. He added that about 39 percent of eligible residents have received at least one shot.

“The people who wanted to get vaccinated, the people who were clamoring to get vaccinated, got vaccinated,” Osur said. “Every week we have thousands of appointments that are going unfilled.” The county has launched a survey to try to find out why, he said.

In Fresno, where only about half of available vaccination slots are being filled, Fresno County Division Health Manager Joe Prado said “the demand isn’t there and so supply is no longer an issue really.”

Officials in some areas are using incentives such as free lunches or coupons “just to get people to walk in, those who are kind of on the tipping point, and this would be just an extra incentive just to convince them to spend a little bit of time with us to get their vaccine,” Fresno County health officer Dr. Rais Vohra said Thursday.

Public health officials have been working to overcome barriers to accessing the vaccine in underserved communities and addressing vaccine hesitancy.

Newsom said the pause in the Johnson & Johnson vaccine affects only 4% of California’s vaccine supplies, with most residents receiving two-dose vaccine regimens from Pfizer and Moderna. But some community members have raised concerns about the effect it could have on the public’s overall willingness to get the shot.

Debra Schade, director of the California School Boards Association, said the rare but serious blood clot problems being investigated are spurring questions from parents concerned whether the shots bring the potential of long-term reproductive health issues for their daughters, now that those age 16 and up are eligible.

“I think there’s a level of hesitancy that you’re not aware of,” she told top state health officials Wednesday during a meeting of the Community Vaccine Advisory Committee.

Newsom echoed health officials in noting the rarity of the problems being investigated and the relative benefits of being vaccinated compared with the dangers of the deadly infection. But he acknowledged hesitancy cuts across all demographic boundaries and can be spurred by residents’ political leanings.

“We still have hesitancy in all communities,” he said. “We have to work across all that spectrum.”

Kiran Savage-Sangwan, executive director of the California Pan-Ethnic Health Network, told health officials Wednesday that residents have also raised concerns about costs, though the vaccine is free.

“People are used to not thinking health care is free, right, so I think it’s taking a lot to make sure people understand, even if you don’t have insurance, even if you’re undocumented, the vaccine is free,” she said.

MORE NEWS: Returning Thanksgiving Travelers Encounter Few Delays At Local Airports

© Copyright 2021 CBS Broadcasting Inc. All Rights Reserved. The Associated Press contributed to this report.