The first vials of the coronavirus vaccine were shipped Sunday, paving the way for inoculations to begin across the country this week.

Nearly 3 million doses of the Pfizer-BioNTech vaccine are being shipped out over several days, with the first wave of shipments set to arrive at 145 facilities Monday, marking the beginning of a massive logistical effort to stop the rampant spread of the virus, which has so far killed more than 298,000 Americans. The vaccine will arrive at nearly 500 additional sites on Tuesday and Wednesday.

But even as state officials scrambled to distribute the first doses, they criticized the federal government for a lack of transparency and limited financial help, warning that both could hamper efforts to quickly vaccinate the most vulnerable populations, including health-care workers and the elderly.

Some White House staff members will be among the first wave of people in the United States to receive coronavirus vaccinations, a Trump administration official said Sunday night. The White House declined to say whether President Trump, who contracted the coronavirus earlier this year, would receive the vaccine.

“Senior officials across all three branches of government will receive vaccinations pursuant to continuity of government protocols established in executive policy,” National Security Council spokesman John Ullyot said in a statement. The administration has not shared when Trump will get a dose. Since contracting the virus, Trump has repeated claims that he is “immune,” but experts are not yet certain about how long immunity lasts.

Late Sunday night, Trump tweeted: “People working in the White House should receive the vaccine somewhat later in the program, unless specifically necessary. I have asked that this adjustment be made. I am not scheduled to take the vaccine, but look forward to doing so at the appropriate time.”

On Monday afternoon, Health and Human Services Secretary Alex Azar will be at George Washington University Hospital when five of its health-care workers receive the vaccine, a senior administration official said late Sunday.

The hospital alone decided who would be at the head of the line. Azar will not receive a shot but plans to do so at some point to help advance public acceptance of the vaccine, the administration official said, speaking on the condition of anonymity for planning purposes.

“This is the kickoff of a series of events you will see from public health officials that are designed to highlight confidence both in the vaccine and in the process America has to distribute the vaccine,” the official said.

As the vaccine doses made their way to hospitals Sunday, Centers for Disease Control and Prevention Director Robert Redfield gave the final nod, greenlighting the decision to recommend Pfizer’s vaccine for those 16 and older.

Additionally, the governors of California, Washington, Oregon and Nevada announced Sunday that an independent review of the Pfizer vaccine found it was safe for public use. They said the vaccine was on the way but did not give a specific estimate for when the first shots would be given.

As the vaccine arrived at a Louisville hub for distribution across the east coast Sunday, Kentucky Gov. Andy Beshear (D) moved up his timeline, announcing that immunizations could begin as early as Monday. New Jersey Gov. Phil Murphy (D) said Sunday that the first vaccines are expected to be administered Tuesday at University Hospital in Newark.

Despite the rapid rollout of the Pfizer vaccine, it will be months before immunizations have any effect on the pandemic in the United States, where cases are surging. As of Sunday, more than 16.3 million people in the United States have tested positive, and an average of 2,470 people died of the virus every day for the past week, a pandemic record.

Officials stressed that a large proportion of the nation’s population — about 70 to 80 percent — will need to get the vaccine before herd immunity is achieved.

Moncef Slaoui, chief science adviser to the White House’s effort to develop a vaccine, said officials hope to “reach that point between the month of May and the month of June.”

“All in all, we hope to have immunized 100 million people, which would be the long-term care facility people, the elderly people with comorbidities, the first-line workers, the health-care workers,” he said in an interview on “Fox News Sunday.” “It’s about 120 million people — we would have immunized 100 million people by the first quarter of 2021 with two doses of vaccines.”

Health and Human Services Secretary Alex Azar detailed what could come in the weeks and months following the initial vaccine shipments. He said the plan is to have 20 million people vaccinated by the end of December, up to 50 million by the end of January and 100 million by the end of February. That includes plans for a second vaccine, developed by Moderna, which is expected to gain emergency authorization from the Food and Drug Administration soon.

The FDA gave emergency use authorization for Pfizer and BioNTech’s vaccine on Friday for people 16 and older, and Moderna’s vaccine is expected to be authorized following a review scheduled for Thursday by the agency’s independent advisers.

“We’ll be getting more and more Pfizer product, and we’ve got 12½ million Moderna product, assuming that we get approval at the end of this week on Moderna, that we’ll ship out very soon thereafter,” Azar said during an interview with CBS News’s “Face the Nation.”

He was also asked by host Margaret Brennan whether he believes President-elect Joe Biden’s team will be able to meet the goals, and Azar appeared to acknowledge that the incoming Biden administration will take over the process.

“If they carry forward with the plans that we’ve put in place, 100 million shots in arms by the end of February is very much in scope,” Azar said.

Officials hoping to bolster confidence in the vaccine worry that such a large immunization effort could be hindered by skepticism.

Francis Collins, director of the National Institutes of Health, said the level of potential vaccine hesitancy in the nation is of “great concern for all of us.”

During an interview on NBC News’s “Meet the Press,” he urged viewers to “hit the reset button on whatever they think they knew about this vaccine that might cause them to be so skeptical.”

“The data is out there now. It’s been discussed in a public meeting, all the details of the safety and the efficacy for anybody who wants to look,” he said, adding: “I think all reasonable people, if they had the chance to sort of put the noise aside and disregard all those terrible conspiracy theories, would look at this and say, ‘I want this for my family. I want it for myself.’ People are dying right now. How could you possibly say, ‘Let’s wait and see,’ if that might mean some terrible tragedy is going to befall?”

There’s also particular concern about addressing any vaccine hesitancy in communities of color, especially because they have been disproportionately affected by the pandemic.

NBC’s Chuck Todd asked Collins to respond to concerns from a health-care worker who said she hopes people who look like her and other Black doctors in the community also will help generate trust in the vaccines.

“She’s absolutely right. For somebody like me to say, ‘You should be signing up for this vaccine,’ okay, a White guy who works for the government. Sure, that isn’t necessarily going to be the voice that people need to hear if they’re skeptical,” Collins said. “We are working closely with health-care providers, especially those in communities of color, and trying to make sure that all of those messages are ready to go.”

Craig Timberg and Tory Newmyer contributed to this report.