At the time of the signing of the Declaration there was no such thing as “Unitarianism” or “Universalism”. These came later. Unitarianism in the US emerged in the early years of the 19th Century, while the Universalist Church wasn’t formed until 1793 - mainly by recent immigrants.
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 (17201766), 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 (17051787), 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 (16981787) of Hingham, Samuel West (17301807) of New Bedford, Thomas Barnard (17481814) of Newbury, John Prince (17511836) and William Bentley (17581819) of Salem, Aaron Bancroft (17551836) 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 (17591853) 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 17831785, 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 Plymouththe congregation founded by the Pilgrims in 1620accepted 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.