The 26-year-old David -- who is in the final 16 -- told the judges during his first audition that he was singing for his birth mother -- whom he'd never met -- who gave him up for adoption from Brazil as a baby.

Sources close to David tell TMZ when his episode of "X" aired in Brazil, a woman named Luciene Lima recognized the baby pics shown in David's segment and had a gut feeling he was hers.

We're told Luciene went through the Brazilian court system to trace her adoption -- and her findings led her back to David. Luciene, not knowing how to reach out to her long lost son, contacted the local media.

Our sources say a local paper was able to track David down in the U.S. and tell him about his mother.

We're told a DNA test has not been performed, but so far everything matches: the birth certificate, the orphanage David came from and the timeline.