Born and raised in Billings, Montana, Neibauer eventually relocated to Nebraska, along with his family. At the University of Nebraska, he earned a varsity letter in four sports. Neibauer was drafted in both the regular and secondary phases of the 1966 Major League Baseball Draft by the Cleveland Indians and Braves, respectively, and he signed with Atlanta after failing to sign a contract with Cleveland. In 1966 and 1967, he pitched for the Austin Braves of the Texas League, before gaining a promotion to the International League's Richmond Braves in the latter year. The Braves promoted Neibauer again in 1969, this time to the Major Leagues; he made his first career appearance on April 12 in a game against the Cincinnati Reds. In his first Major League season, Neibauer pitched in 29 games and had a 1–2 win–loss record and 3.90 ERA in innings pitched. In addition, he pitched one inning in Game 2 during the 1969 National League Championship Series, allowing no hits or runs.