On Wednesday, police said the baby - now a woman - has been found.
Carlina White was just 19 days old when she disappeared from Harlem Hospital on Aug. 4, 1987. Police searched for her kidnappers but never found enough evidence to charge any suspects. Her mother, Joy White, always had a feeling that her baby was alive, her family said.
On Jan. 4, a woman known as Nejdra Nance, who was raised in Bridgeport, Conn., and now lives in Atlanta, contacted White, sending along baby photos that looked nearly identical to shots of Carlina posted on a missing children's website. Nance told White she thought she may be her daughter.
Nance had never been able to find her birth certificate.
"She said she just had a feeling, she felt different from the people raising her," said Nance's maternal grandmother, Elizabeth White, 71. "She searched, and then she found Joy."
Joy White contacted the New York Police Department to see if it could help investigate whether the woman was really Carlina White.
"It sounded legitimate and credible, so I had missing persons reach out to her," said Detective Martin Brown, who fielded the call. DNA tests performed on Joy White, her ex-husband, Carl Tyson, and 23-year-old Nance matched, police said. Nejdra Nance was Carlina White.
As part of their investigation, police are talking to retired detectives who handled the case years ago. Because she was so young when she was kidnapped, it's impossible for Nance to know if she has lived with the same family the entire time.
Nance saw her biological family in New York Wednesday night, said Elizabeth White, but they had already reunited once recently, when Nance came to New York with her 5-year-old daughter, Samani.
"It was wonderful, she didn't even seem like a stranger, she just fit right in," Elizabeth White said. "We all went up there, we had dinner together, her aunts were there. She brought her beautiful daughter. It was magic."
Elizabeth White said she didn't ask Nance too many questions about how she grew up or how she knew she was not a member of the family with whom she lived. She didn't want to push Nance too much.
"That will all come," Elizabeth White said of the history. "What's important now is our baby girl is home. She's home."
"We was always thinking that one day, she would come back," Elizabeth White told CBS News correspondent Seth Doane, even all these years later. "I never gave up hope," White told Doane, "and I never thought that she was dead or anything."
Authorities say the kidnapper could still face federal charges, though no arrest has been made.