Gálvez was signed by the Los Angeles Dodgers of the National League in 1981, and made his Major League (MLB) debut in 1986 with the Dodgers. He played in 10 major league games that year, but was demoted to the minors at the start of the 1987 season and never appeared in another MLB game. Over the next several years, Galvez also suited up for minor league affiliates teams of the Detroit Tigers, Minnesota Twins, New York Yankees of the American League, along with National League teams Montreal Expos and the Chicago Cubs in the 1980s and early 1990s.\n', '

In 1994, Galvez signed with the Brother Elephants of the national capital of Taipei in the Chinese Professional Baseball League on the island nation of Taiwan (with the Nationalist government of the Republic of China since 1949 after the Chinese Civil War). In two full seasons with the Elephants, he had a 26–16 record with an ERA of 2.53 and 203 strikeouts in 370 innings pitched. \n', '

He traveled to Japan in 1996 where baseball had a fevered fan base of followers since the early 20th century shared with the Americans who introduced the sport. Galvez was signed during spring training by the Yomiuri Giants, the most famous Japanese baseball team in the Nippon Professional Baseball League. He ended up with 16 wins, tying teammate Masaki Saito for the most wins in the Central League of the NPBL. The Giants won the Central League pennant that year, playing in the Japan Series of the championship tournament.\n', '

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