About 300,000 kids under 5 have gotten at least 1 dose of COVID vaccine so far

By the end of Thursday, roughly 300,000 children under the age of 5 years old will have received at least one dose of a COVID-19 vaccine, a senior Biden administration official told ABC News.

The 300,000 shots in arms so far for kids under 5 is about 1.5% of the roughly 19.5 million U.S. children 4 years old and younger.

It's a modest start to vaccinating this youngest yet age group -- a drip-drip the White House says they are not surprised by.

"That number in and of itself is very much in line with our expectation, and we're eager to continue working closely with partners to build on this start," the senior administration official said.

This latest data also comes on the heels of a holiday weekend, with lots of families traveling and not thinking about a trip to the pediatrician while on vacation. Moreover, data takes time to flow in, and there could be an increase in the weeks ahead, especially ahead of the school year.

"Even before these vaccines officially became available, this was going to be a different rollout, it was going to take more time," the senior administration official said, citing that parents in this younger age range "overwhelmingly prefer to get their kids vaccinated at a place that they know, with health care providers they know, in familiar settings," and many may opt to get their kids the shots during a regular or annual wellness visit.

The White House is counting on those moments and opportunities for parents to speak with their child's doctor and get answers to whatever outstanding questions they may have.

Even before COVID vaccines were authorized for children under 5, polling presaged the apprehension we're seeing play out in the gradual immunization rate now.

A Kaiser Family Foundation poll from early May -- before the vaccines were authorized, recommended and available -- found that less than a fifth of parents with children under the age 5 -- 18% -- reported they were eager to get their child vaccinated right away.

More than a third of parents -- 38% -- said they planned to wait to see how the vaccine works for others, while 27% of parents reported that they will "definitely not" get their child vaccinated, and 11% said that they will only do so if they are required. More than half of parents said that they feel they do not have enough information about the vaccines' safety and efficacy for children under age 5.

With vaccination rates in kids under five starting out slow, the White House expects moments of acceleration spurred on by the academic calendar -- or potential variant surges -- including around back-to-school time and holidays.

This week, new infections among children are back on the rise for the first time in nearly two months -- and surges can be "part of the conversation starter for a lot of parents about these vaccines," the administration official said.

The senior administration noted there will always be holdouts no one can force to take the shot. However, the official said, "we have a really robust kind of engagement strategy" to "work through people's concerns."

"I think that it's absolutely expected that once the school year starts, there will be unvaccinated children and vaccinated children," the official said. "And I think that that's going to be part of the dynamic that we're working through."

Even if young kids get their first shot this week, some may not be fully immunized by the academic year's start, when vaccinated and unvaccinated children may commingle in the classroom.

The administration official noted that while increasing cases may be a "motivator," it will vary by demographic.

The White House will continue to lean on "trusted messengers" within specific communities they see as having a great impact, like family doctors and pediatricians.

The White House is working with the Sesame Workshop, the nonprofit educational organization behind Sesame Street, to get the word out -- including a PSA from Elmo -- and have launched a partnership with the National Diaper Bank Network to distribute educational materials.

The question of vaccine mandates for school for this young age group will remain up to states.

ABC News' Eric Strauss, Arielle Mitropoulos and Sony Salzman contributed to this report.