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If you are referring to "Link" from The Legend of Zelda series, there is more than one.

His balls is never given in any games.

However, if you want to know when the character itself was conceived; Link was born on July 26th, 1987

I basically assume that there is no exact dates & years in Hyrule, but in the Minish Cap game, it says that the Picori/Minish vist Hyrule every 100 years/century, on the day of the Picori Festival is held, which is NEVER given!