That was 19 seasons ago. Now, Giambi is 42 years old and starting to hear age-related records.
During Wednesday's 6-3 loss to the Red Sox, Giambi launched a solo home run in the sixth inning, marking his first long ball in a Cleveland uniform. It also made him the third-oldest Indians player to belt a home run, dating back to 1916. Giambi trails only Sam Rice (44 years old, 1934) and Dave Winfield (43, 1995) in that respect.
"It makes me laugh," Giambi said. "I don't think of myself that old. I know I am, but I don't think of myself like that."
Giambi's home run came as the second shot in a series of back-to-back bombs with Nick Swisher. Giambi spent the first eight games of this season on the 15-day disabled list, but has had a lot of loud outs -- to go along with Wednesday's home run -- in his first eight at-bats with Cleveland.
Giambi, who is serving as a part-time designated hitter and pinch-hitter this year, has been pleased with how he has felt early on with his swing.
"I've been excited where my swing has been for missing that time at the beginning of the year," Giambi said. "I was kind of a little bit surprised. When I got in there that first game [Sunday], I didn't quite know where I'd be. I took out of there a lot of confidence with where my swing was at.
"I was excited about [the home run]. It's nice to get a little results and get the first one out of the way."
Giambi has kept the first home run ball with each of the teams he has played on, and he was able to have the ball from Wednesday retrieved so he can add it to his trophy case. The homer was the 430th shot of Giambi's career, putting him 43rd on baseball's all-time list, ahead of Mike Piazza (427) and behind Cal Ripken Jr. (431).
"The guys you start to pass now are pretty impressive," Giambi said.
Jordan Bastian is a reporter for MLB.com. Read his blog, Major League Bastian, and follow him on Twitter @MLBastian. This story was not subject to the approval of Major League Baseball or its clubs.