NEW YORK (CNN) -- For more than a half-century Jerry and Marilyn Damman wondered what happened to their 2-year-old boy, who mysteriously vanished into thin air outside a Long Island bakery.

Steven Damman and his sister disappeared from outside a bakery in 1955. His sister was found safe.

Now, 54 years later, a Michigan man claims he is the missing child whose name was Steven Damman.

Within the last six months, the unidentified man contacted Nassau County, New York, police and said he had credible evidence that would link him to the case of the missing toddler, according to police Detective Lt. Kevin Smith. Nassau County police turned the case over to the FBI in Detroit.

So far, authorities will not release the Michigan man's identity and won't say why he believes he is Steven Damman. The FBI is conducting DNA testing, Smith said.

Sandra Berchtold, spokeswoman for the FBI Detroit bureau, said only, "The FBI investigates all leads in kidnapping cases, but cannot confirm or deny the existence of an investigation in this matter."

In 1955, Marilyn Damman took her toddler, Steven, and his baby sister, Pamela, to a bakery in East Meadow. The mother went inside to do some quick shopping, leaving her 2-year-old and baby girl in the stroller outside. But when Damman returned, her children were gone. A short time later, blocks away, the baby girl was found unharmed and the stroller was intact, but Steven was missing, Smith said.

Thousands of searchers looked for the toddler, but the boy was nowhere to be found. Hitting one dead end after the next, the Dammans packed up and moved from New York back to Iowa, Jerry Damman said.

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And until now, they thought there was little chance of ever seeing their son again.

Jerry Damman, who lives on a farm in Iowa, told CNN, "You never give up hope, [but] things dim after all those years."

He said he isn't ready to comment on the latest developments for various reasons. Damman says authorities have contacted him, but he has not yet given DNA samples.

A few years back, Steven Damman's sister gave a DNA sample in connection with the 1957 Philadelphia case of a young boy's body found in a box. In that case, all indications were it was not Steven Damman.

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