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Why not going to the very beginning?

The pilgrims came escaping from the way of worship imposed in England.

The pilgrims didn't come and started a new religion, but they wanted to worship "the same god" in their way. They might started new religious "denominations" from the same religion, this is to say, from worship to the "same god".

The religion was the same: the Judeo-Christian religion.

The Christian religion was expanded in Europe as the Catholic Church.

A dude didn't agree with the way of worship of the Catholics and nailed his protests in a monastery door, since then, the groups who separated themselves from the Catholic Church were called "Protestans".

The protestans also were divided in many denominations, but they still were Christians.

The first travelers were Anglicans, Quakers, Puritans, etc. Their religion was based in or accepted the teachings of Christ.

Centuries later, when the issue of "freedom of religion" was included in the Constitution, the meaning was in reference to the same god, but with different ways of worship.

The Constitution wasn't directed in its origin to include the Muslim religion as an example. This is a modern interpretation, the same as well it happens with the phrase "WE the PEOPLE" that for Adams didn't include women, poor people, slaves, children and more, but only people of influence and power.

So, it can be say that the Unites States of America started as a Christian nation.

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If you go to the Washington Mansion in Mount Vernon, Virginia, you can read in one of the articles posted in the walls, that the freedom of religion was directed to be to the god of the bible, not so to any other god.