McAllen, Texas — Most of the 13 migrant boys waiting inside the small airport in this south Texas city were still wearing the gray sweatpants and sweatshirts the U.S. government gave them after they crossed the southern border alone. The 5 p.m. takeoff to Houston earlier this month had been delayed by about an hour, leaving them at risk of missing their connecting flight. Once the plane arrived, the boys boarded the commercial flight alongside three government contractors and, coincidentally, this reporter. Families with young children released from Border Patrol custody were also there. It was their first time on a plane. Once they landed, the boys rushed through Houston’s sprawling airport to gate C10, where their flight to Newark, New Jersey, was scheduled to take off within minutes. They were relieved to find it was also delayed. The boys killed time, talking about Manchester United’s resounding 6-2 victory over Roma earlier that week. The 13 young migrants landed in Newark after midnight. Several families were waiting in the arrivals area, one of them holding a “welcome to New York” poster. One of the teens spotted his family and rushed to hug them. Three other boys followed, lining up to embrace their parents and relatives, some of whom they had not seen in years. They held onto their loved ones for more than a minute. A fellow passenger who had met one of the boys on the flight cried while recording the reunions on her phone. Elmer, 14, had not seen his mother, María, since she left Honduras in 2018. She said she could feel Elmer’s heart beating fast and his hands trembling. “I cried. It was something special,” María told CBS News in Spanish. “I ran and hugged him. My little boy had grown up. I thanked God for keeping him safe. It’s a beautiful feeling to see your son knowing that he was exposed to danger for so long.” In the background, Elmer hugs his sister as his mother records in Newark Liberty International Airport on Sunday, May 2, 2021. CBS News Elmer then turned to hug his 17-year-old sister. “They have been really close since he was born and had never separated,” María said, who also brought her 1-year-old baby to the airport. The reunited family made it to New Haven, Connecticut, around 4 a.m. Elmer said he took a shower and got ready to sleep alongside his mother. “I was filled with a lot of happiness and emotion,” Elmer told CBS News. Elmer couldn’t sleep. María said he was still awake at 6 a.m. “When I opened my eyes, he was looking at me. I don’t think he expected to be with me again,” María said. “But I had promised him that I would fight to make it happen.” “Around-the-clock effort” Elmer’s long-awaited reunification with his mother and siblings is part of an unprecedented U.S. government effort to place the record number of unaccompanied children who have crossed the southern border in recent months into the homes of relatives in the U.S. During President Biden’s first full three months in office, more than 45,000 unaccompanied migrant children entered U.S. custody along the southern border, according to government figures. The Biden administration has been sheltering these children, refusing to revive the Trump-era policy of expelling them under a pandemic-related emergency order known as Title 42. Shelter space for unaccompanied children started dwindling in February. By March and early April, Border Patrol facilities that are not designed to hold minors were severely overcrowded, holding nearly 5,800 unaccompanied children at one point. Elmer said he spent a week at the Donna, Texas, Border Patrol holding facility for migrant children, the largest of its kind. He said it was packed with other unaccompanied children and families. He remembered getting little rest and dreading servings of burritos that were often still semi-frozen. Overcrowding at these facilities has since eased and the number of unaccompanied children in Border Patrol custody has plummeted by over 90%, falling below 600 this week. However, there are still more than 20,000 unaccompanied children in the care of the Department of Health and Human Services (HHS), which houses them until it can release them to sponsors, who tend to be family members in the U.S. While shelters overseen by HHS are much better suited for children than Border Patrol facilities, as of last week, more than 13,000 of the unaccompanied youths in the department’s custody were being held in convention centers, work camps, military bases and other emergency sites that are not licensed to care for minors, according to internal data reviewed by CBS News. HHS now has the formidable task of locating and vetting sponsors for more than 20,000 children currently in custody, as well as the hundreds of minors it continues to receive from Border Patrol daily. Between February and April, HHS’ Office of Refugee Resettlement received 33,700 unaccompanied children, with each month setting a historic record, according to agency figures obtained by CBS News. Between Mr. Biden’s inauguration and this week, HHS placed more than 20,000 children with sponsors, according to a department official. In a photo taken on March 27, 2021 unaccompanied children, immigrants who arrived illegally across the Rio Grande river from Mexico, stand at a makeshift processing checkpoint before being detained at a holding facility by border patrol agents in the border city of Roma. ED JONES/AFP via Getty Images HHS has been increasing its discharge rate in recent weeks. In late January, it released an average of 89 minors daily, the department official said. Recently, HHS has been placing an average of 608 children with sponsors per day. The length of time children are spending in HHS care has also decreased. According to the HHS official, migrant minors are spending about 29 days in the department’s care before being released, compared to the 42-day average in late January. The refugee office has created an expedited release process for children who have parents willing to care for them in the U.S. It has also been paying for the travel costs of minors and their sponsors to facilitate the reunification, and allowed case managers to fill out application forms for potential sponsors. Neha Desai, a lawyer representing migrant youth in a landmark court case, said HHS has made progress in speeding up the release of children, but noted that more can be done. She said HHS could waive fingerprint requirements for uncles, aunts and cousins of children in care, just like the department has done for parents and primary caregivers, like grandparents. “Currently, there are numerous children in custody simply because the government is awaiting results from fingerprints, even though public records checks have already been completed,” Desai, of the National Center for Youth Law, told CBS News. “Waiving the fingerprint requirement for immediate relatives who did not previously serve as the child’s primary caregiver, would improve ORR’s ability to swiftly, yet safely release children to sponsors.” HHS said it is undertaking an “incredible around-the-clock effort” to rapidly reunite migrant children with their families. But an HHS official said the department is doing so while maintaining sponsor-vetting safeguards designed to protect minors. All potential sponsors undergo background and sex offender checks. “I can feel really confident that we have not cut corners, that we have found efficiencies and that we have made things more streamlined,” an HHS official told CBS News. “We want to make sure that we’re doing safe discharge and we’re doing timely discharge.” “It’s very beautiful” María, who cleans a building in the Bridgeport area at night, said she fled Honduras with her teenage daughter in 2018 due to political persecution stemming from her advocacy against the conservative Honduran government. In 2019, a U.S. immigration judge granted her asylum, but the Trump administration appealed the decision, delaying her case, she said. Because of the appeal, María said she was not able to petition for Elmer to come to the U.S. legally. She said she had been wanting him to leave Honduras as he was staying in a remote area and not attending school. “I tried to bring him legally, but couldn’t,” María said. “My son spent two years without going to school. He lived with his 90-year-old great grandmother, who could not care for him. That’s what made me make the decision, despite my fear about the journey.” Elmer’s trek to the U.S. border spanned 30 days. He said it wasn’t easy, but noted he pushed forward with the hope of reuniting with his family. María said she constantly worried about his safety, noting the smugglers he was traveling with abandoned him and other youths in northern Mexico. “I don’t think he was fully aware of the danger, but I felt it,” María said. “There are a lot of people who want to harm migrants.” María and Elmer, 14, in New Haven, Connecticut. They reunited earlier this month after a more than 2-year separation. Photo provided to CBS News If the government drops its appeal on María’s asylum case, Elmer would automatically be eligible for permanent U.S. status. On Wednesday, Elmer had his first day of school in the U.S. It was virtual, but he’s hoping to start attending in-person classes next week. He said he’s looking forward to math class, his favorite subject. “It’s very beautiful,” Elmer said when asked if he likes the U.S.