Daye was born in Sutton, Surrey London, and emigrated on June 7, 1638 to Cambridge Massachusetts on board the "John of London" with his wife Rebecca (Bordman - from a previous marriage) (died October 17, 1658), sons Stephen, Jr. (died December 1, 1639), Matthew (died May 10, 1649), and stepson William Bordman (died March 25, 1685), and three household servants. In 1638 he is recorded as being a locksmith by profession who was under financial contract to Reverend Joseph Glover to repay the loan of £51 for ship transportation for himself and his household and the cost of purchasing iron cooking utensils. Further, he was contracted to set up a printing press at Glover's home in Cambridge, Massachusetts and to be paid wages according to Massachusetts custom.
Glover died on the ship John of London during the voyage, but Daye was legally bound to fulfill his contract setting up the printing press with the aid of his sons and stepson in the home of Rev. Glover at Cambridge. Elizabeth Glover, the widow, was the legal owner of the press and Daye's debt and contract upon the death of her husband. In 1639, it is generally thought or cited in the survey of the literature that Daye printed his first work, The Freeman's Oath, a broadsheet. However, this work may have actually come second following the printing of the first almanac composed by William Pierce. Pierce's almanac, as was typical, commenced with the month of March, which according to English law and custom was the first month of the year, rather than the Gregorian calendar that began in January.
Consequently, Daye must have printed Pierce's almanac prior to the English first of the year that began on March 15. In 1640, he printed the Bay Psalm Book, the first book published in the American colonies. The next year, 1641, Daye was rewarded for his work with three hundred acres of land.