Massachusetts, New Hampshire, and Connecticut each had an "established church" from the time of the original Puritan settlement. That is, a church recognized as the official church of the country, supported by taxation and with attendance or at least membership required. The practice of different religions was suppressed, and Massachusetts even executed several Quakers.
Those churches were "Congregrationalist": Calvinist in theology, but with an organization different from the Calvinist Presbyterian church of of Scotland, or the Calvinist Dutch Reformed Church, which had been established in "New Netherlands" and survived in New York.
Pennsylvania was founded by Quakers, who rejected any form of religious "establishment". The many German immigrants to Pennsylvania were mostly Lutherans or Baptists.
Rhode Island was founded by dissenters from the neighboring Puritan colonies, and practiced complete religious toleration: one of the earliest Jewish congregations in America was formed there.
In the mid-1700s, the evangelical movement known as "Methodism" came to the American colonies, and won many followers, who set up independent churches.
Maryland was founded by Lord Baltimore as a refuge for Catholics. Though Maryland was majority Protestant, a significant body of Catholics remained there.
The Southern colonies were largely settled by Anglicans, but AFAIK there was no religious "establishment" in any of them.
So from the very earliest days of "America", there was great religious diversity, and most people were not under the jurisdiction of any "established" church. Even in Massachusetts, the "established" Congregational Church was bitterly divided between "liberal" Unitarians and traditionalists. (The Church was disestablished in 1833 by traditionalists when Unitarians became the majority.)
Thus there never was any possibility of a "Church of America".