Unitarianism in the United States followed essentially the same development as in England, and passed through the stages of Arminianism, Arianism, to rationalism and a modernism based on an acceptance of the results of the comparative study of all religions. In the early 18th century Arminianism presented itself in New England, and sporadically elsewhere. This tendency was largely accelerated by a backlash against the “Great Awakening” under Jonathan Edwards and George Whitefield. Before the War of Independence Arianism showed itself in individual instances, and French influences were widespread in the direction of deism, though they were not organized into any definite utterance by religious bodies.
As early as the middle of the 18th century Harvard College represented the most advanced thought of the time, and a score or more of clergymen in New England preached what was essentially Unitarianism. The most prominent of these men was Jonathan Mayhew (1720–1766), pastor of the West Church in Boston, Massachusetts from 1747 to 1766. He preached the strict unity of God, the subordinate nature of Christ, and salvation by character. Charles Chauncy (1705–1787), pastor of the First Church from 1727 until his death, the chief opponent of Edwards in the great revival, was both a Unitarian and a Universalist. Other Unitarians included Ebenezer Gay (1698–1787) of Hingham, Samuel West (1730–1807) of New Bedford, Thomas Barnard (1748–1814) of Newbury, John Prince (1751–1836) and William Bentley (1758–1819) of Salem, Aaron Bancroft (1755–1836) of Worcester, and several others.
The first official acceptance of the Unitarian faith on the part of a congregation was by King's Chapel in Boston, which settled James Freeman (1759–1853) in 1782, and revised the Prayer Book into a mild Unitarian liturgy in 1785. The Rev. William Hazlitt (father of the essayist and critic), visiting the United States in 1783–1785, published the fact that there were Unitarians in Philadelphia, Boston, Charleston, Pittsburgh, Hallowell, on Cape Cod, and elsewhere. Unitarian congregations were organized at Portland and Saco in 1792 by Thomas Oxnard; in 1800 the First Church in Plymouth—the congregation founded by the Pilgrims in 1620—accepted the more liberal faith. Joseph Priestley emigrated to the United States in 1794, and organized a Unitarian Church at Northumberland, Pennsylvania, the same year and one at Philadelphia in 1796. His writings had a considerable influence.
Thus from 1725 to 1825, Unitarianism was gaining ground in New England, and to some extent elsewhere
What this list shows me is that America's religious makeup has gone thur vast changes since this nation was founded. Anglicians (then the largest of adherents) and Congregationalists are now only a small percentage of Americans. Catholics, Baptists, and Lutherans are now major influences in the United States. In the 1700s, their presence was marginal.
“Unitarian tendencies” existed - that is, various doctrinal deviations within the Congregational church - but these various tendencies didn’t all emerge, nor were they all held by individuals (as opposed to individuals holding perhaps one or two of them), until well after 1776.
Unitarianism didn’t even emerge as a movement at the earliest until 1805 when an important chair of theology at Harvard was filled by a Congregationalist with some Unitarian tendencies. It didn’t coalesce into a denomination until 1825, although William Ellery Channing’s sermon at the investiture of Jared Sparks in 1819 marked the point where all the Unitarian heresies were self-consciously presented as an alternative to orthodox Congregationalism. So, intellectually, 1819 is a clear starting point for Unitarianism, while institutionalally 1825 would be the date.
No signer of the Declaration was a Unitarian or a Universalist. There may have been a couple of signers who had some affinity theologically for some element or other of Unitarianism or Universalism, but that doesn’t mean that they were Unitarians or Universalists any more than by agreeing with a plank or two of the Communist Manifesto you become a Communist.