Young U.S. children will start getting vaccines on Tuesday, but hurdles remain.

Parents who experienced more than two years of anxiety may feel some relief on Tuesday, as much of the United States begins administering coronavirus vaccines to children younger than 5, allowing babies and toddlers to more safely explore the world.

“We’re very excited,” said Rachel Lumen, a lawyer in Kent, Wash., and the mother of Athena, who is almost 3, and Ozette, who is 7 months old. “The faster it happens, the faster we’re able to get out there.”

Last week, after multiple delays, the Centers for Disease Control and Prevention signed off on Moderna and Pfizer-BioNTech vaccines for children as young as 6 months, expanding immunization to almost all Americans.

“It marks an important moment in the pandemic because it was the last group, the last demographic, that had not had the opportunity to keep themselves maximally safe,” Dr. Bob Wachter, the chair of medicine at the University of California, San Francisco, said. “It’s not likely to turn the tide in terms of where we are generally in the pandemic, but for the parents of those kids, it’s an important watershed.”

The start of vaccination for young children is a milestone, but that group never faced as much risk from Covid-19 as older Americans, and this phase of the nation’s immunization effort has been met with mixed emotions.

A recent Kaiser Health poll found that just one in five parents will get their young children vaccinated immediately. Vaccines have lost some potency against infection by new variants, and although the shots continue to protect against the worst outcomes of Covid-19, many parents remain hesitant or believe incorrectly that their children will not be infected again if they have already gotten sick.

Andressa Carrasco, a resident of Fort Lauderdale, Fla., said she and her husband had been cautious since the pandemic broke out. Fears that their son, Sebastian, now 18 months old, would get sick kept them from sending him to day care. For the first year of his life, he scarcely saw anyone outside their household.

They delayed making plans and “missed so many things,” thinking if they could hold out just a little longer, they might be able to get Sebastian vaccinated before visiting loved ones. But Ms. Carrasco said that over time she started to lose hope. She and her husband decided to travel to Peru for a family wedding.

“The last six months we were kind of over it,” she said. “We just kind of gave up.”

All of the Carrascos had the coronavirus last week.

Still, Ms. Carrasco said she would take Sebastian, who is recovering from a fever, to be vaccinated as soon as his pediatrician recommends.

Even parents in states where leaders enthusiastically encouraged residents to sign up their children for shots have encountered hurdles.

Ms. Lumen, the mother in Washington State — where Gov. Jay Inslee applauded the news that vaccines had been authorized for young children — said she quickly called the pediatrician’s office to set up a vaccination appointment for her two young children.

But she said the doctor’s office did not know when they would actually be able to start administering the vaccines. She also called Walgreens, but as is common for pharmacies, it was not offering appointments to children under 3.

“The moment we can find a place to get our kids vaccinated, we will,” she said.