Signed as an undrafted free-agent by the White Sox in 1965, Nyman began his professional career that year with the Sarasota Sun Sox. With them, he went 16–11 with a 2.81 ERA in 30 games. In 192 innings pitched, he walked 137 batters. He split the 1966 season between the Deerfield Beach/Winter Haven Sun Sox, Fox Cities Foxes and Lynchburg White Sox, going a combined 6–11 with a 2.46 ERA in 20 games. In 1967, he played for the Evansville White Sox, going 7–4 with a 2.74 ERA in seven games.\n', '

Nyman spent most of the 1968 season with the Hawaii Islanders, going 7–5 with a 3.09 ERA in 23 games with them. On August 24 of that year, he made his big league debut, facing the Minnesota Twins. He pitched 2/3 of an inning in relief in his first game, allowing a hit and a walk but surrendering no runs.\n', '

His first game would be the only relief appearance of his first big league seasons. He went on to start seven games for the White Sox, throwing a complete game shutout in his first career start. In eight big league games in 1968, Nyman went 2–1 with a 2.01 ERA.\n', '

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