Interesting question. However, it doesn't have an answer you are likely to find appealing. We don't know for certain because if people with actual atheistic beliefs existed in New England during this period, they did so in silence and under the guise of being at least moderately religious. While religiosity amongst Americans was extremely low by the time of the American Revolution's beginning in 1775, religious life amongst early American colonists were extremely high, especially in New England prior to the turn of the 17th century. The story of religious separatist "pilgrims" landing at Plymouth in 1620 is akin to American mythology, this region was settled by folks who were deeply fundamentalist in their beliefs and were seeking a safe haven for people who held similar beliefs. Although religious separatists from the Church of England did first arrive, the Puritans who followed behind them were not looking to break away from the church. Instead, these were people with arguably even more passionate beliefs and wanted to become even more refined in their faith than those still in Britain. However, the story of religion in New England is actually more complicated than what most Americans understand today. I'm going to then try to best explain this answer in two parts. First, talking about what we know about religious and societal dissenters in New England society during this period. Next, I'll discuss Atheism in the 17th century.

Perceived Dissenters in 17th Century New England

Puritans who settled New England through the 17th century were very fervent in their religious beliefs and did not, in any way tolerate dissenters. It was not enough to simply be a "Christian" you had to be the right type of Christian who ascribed to the same beliefs as others living in those colonies. This led to an extremely oppressive view of other types of Christians. A good example of the intolerance that flourished under this is the way that Quaker immigrants interacted with New England's settlers. Quakers, who were fervent in their own beliefs as well, came to the colony in 1656, and multiple Quaker 'leaders' (this is merely an informational title since Quakers claimed to have no religious leaders at all, but merely some members who were more vocal than others) were exiled from the state between 1656 to 1660. Several of these leaders returned, some more than once, leading to harsh reactions from their intolerant neighbors, leading to violent arrests, floggings, and extended jail time where some Quaker prisoners were jailed in drafty cells without blankets or any type of warmth, leading to illness.(1) The violence against Quakers in Boston and its surrounding areas peaked in 1659 to 1661, where Boston's religiously controlled government executed William Robinson, Marmaduke Stevenson, Mary Dyer, and William Leddra of Barbados.(2)

I feel like it is also worth mentioning that persecution against other denominations of Christians were not the only type of persecution that potential Atheists would have seen. Laws against people who are gay also were rampant in New England during this period. The English Sodomy Act of 1533-34 declared the sentence of death for sodomy and bestiality and this law was essentially copied into the New England legal codes in 1648 Massachusetts. That said, records suggest that only one such execution ever took place in America during the 17th or 18th centuries, leaving such laws were largely unenforced.(3) A total of three people are known to have been executed for homosexual charges during the colonial period.(4) The main takeaway from this should be clear -- Puritans were not looking to accept people who were different, had conflicting beliefs, or wanted to live their life even marginally different than regular society. They wanted conformity.

Atheism and Religious Beliefs in 17th Century New England

So why do I mention all this about Quakers when you asked about Atheists? For several reasons. One, is that if a person who grew up in this society witnessed this level of persecution against other Christians than imagine what would happen to someone who was an apostate? The other, is that during this period, the Enlightenment, which spurred new ideas into reflections upon religion, namely Deism and even Atheism was only in the beginning stages. Enlightenment views of religion really would not spread to the Americans until the 18th century, and typically through notable figures like Ben Franklin (whom some historians credit with being the person who brought deism to America.) However, after the reformation in the 16th century, charges of atheism did start popping up (in some areas of the world it was rather frequent) and often times held a sentence of death. But what was atheism back during this period. I'll let historian Leif Dixon explain:

During the sixteenth and seventeenth centuries, the use of this label became more and more frequent, but its meaning was hard to pin down. On one level, the charge of "atheism" came as readily to the lips of 'orthodox" early modern writers as "communist" did to some McCarthy-era Americans -- the term was aggressively elastic, a byword for personal enmity, cultural nonconformity, or political protests--and was thus a phrase of abuse that went well beyond the nominal confines of its technical definition... The atheist was sometimes portrayed as a monster, but he could also represent the idea of a Judas, an enemy within, perhaps a friend, perhaps even oneself.

If there's one take-away that should be taken away from this quote, is that the charge of atheism was an easy charge to levy against someone during this period simply as a blanket term for anyone who could perhaps be untrustworthy. Remember, just a few decades after Massachusetts folks executed Quakers, they also conducted the Salem witch trials which saw the execution of women on anti-Christian charges.

As far as I've seen, there were only handful of charges of atheism levied in New England during this period and they likely could have all been dubious, and none came with a death sentence. (I only had one book at my disposal at the time of this answer, so I may have to dig a little a little more to get details if you desire them). It's also important to take to heart what I said above about atheism, in the way that we understand it today, was not something that was fully developed yet. Skip ahead a century, to around the time of the American Revolution and then you'll start seeing self reported views of religion and God that seem much more agnostic or atheistic.(5)

Hope this answers your question. Please let me know if you have any follow ups.

1. Michael Gandy. Sufferings for Early Quakers Vol. 2 The Ebor Press. 2001.

2. Francis J. Breme & Tom Webber. Puritans and Puritanism in Europe and America, Volume 1. ABC-CLIO. 2005. pp xl

3. Colin L. Talley. "Gender and Male Same-Sex Erotic Behavior in British North America in the Seventeenth Century." Journal of the History of Sexuality, Vol. 6, No. 3 (Jan., 1996), pp. 385

4)Roger Thompson. "Attitudes towards Homosexuality in the Seventeenth-Century New England Colonies" Journal of American Studies, Vol. 23, No. 1, Sex and Gender in American Culture (Apr., 1989), pp. 28

5. Kid, Thomas. God of Liberty: A Religious History of the American Revolution. Basic Books. 2010 pp 232

Edit: spelling error corrections