Allen was born in Springfield, Massachusetts, the son of Joel Allen and Harriet Trumbull. He studied and collected specimen of natural history early in life, but he was forced to sell his relatively large collection so that he could attend the Wilbraham & Monson Academy in 1861. The following year, he transferred to Harvard University, where he studied under Louis Agassiz.
In 1865, he took part in his mentor's 1865 expedition to Brazil in search of evidence of an ice age there, which Agassiz later claimed to have found. After returning to Massachusetts, chronic ill health caused him to return to his family farm in Springfield.
By 1867, Allen's health had improved enough that he went on a flurry of collecting trips, including at Sodus Bay, and in Illinois, Michigan, and Indiana. Upon his return to Massachusetts, he took the position of curator of birds and mammals at Harvard's Museum of Comparative Zoology. In the winter of 1868–1869, he was one of two ornithologists, the other being Charles Johnson Maynard, to explore the relatively unknown state of Florida, which was still very much a wilderness in the late 1860s.

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