Traber went to Loyola Marymount University, where he was First-Team All-American and West Coast Conference Player of the Year. He set a single-season school strikeout record with 156 strikeouts (in 123 innings pitched). In 2000, Traber entered the draft and was picked in the first round (16th overall) by the New York Mets. The Mets were prepared to offer Traber a contract worth $1.3 million, but after an MRI showed some damage to his pitching elbow, he signed a contract worth only $400,000.