There is no specific record of Celebrimbor's date of birth. He is first mentioned late in the First Age dwelling in Nargothrond with his father Curufin. It's impossible to know how old he was at this time, but the fact that there is no account of him before this, and especially that he wasn't present to swear the Oath of Fëanor, suggests that he was born after the Noldor returned to Middle-earth.