So “Indians” is a relatively recent nickname of the 1918-1925 period, and “Green,” at least as adjective, may be as early as the 1860s, when the color was selected. When did “the Big Green” emerge as a complete nickname?
The words “big Green” began appearing in the New York Times by 1911, but only as adjectives describing nouns such as “team,” “line,” “eleven,” “players,” “machine,” “skaters,” “five,” etc. The phrase applied not just to football but all sports, apparently. The most frequent use was “the big Green team” (1911), but “the big Green line” (1911) also was popular. Writers also used “Hanoverians” and many other terms. A September 9, 1916 article from the Fort Wayne News wrote stated that it was “necessary to uphold the fame of the ‘Big Green’ team”; the Atlanta Constitution wrote in a November 20, 1921 headline that “Dartmouth’s Big Green Machine Arrives Early.” This use of “big Green” as an adjective continued into the 1940s.
When was “Big Green” used as a noun phrase on its own? In the shorthand phrasing of newspaper headlines, it appeared by 1916. A November 11, 1916 article in the Times uses the headline “Big Green Practices Here,” for example. The first line of the article, however, used the earlier form when it stated that “The big Green team from Dartmouth arrived here yesterday . . .”
The first use of “Big Green” as we know it today might be in the Times of October 28, 1923, where the article stated that “the Big Green began its march for its first touchdown.” The following football seasons of the early 1920s saw many such uses: “the Big Green, passed [. . .] its way through a stubborn Chicago team here today” (Decatur Review (November 14, 1925)), etc.