Well, you have certainly accurately described the Puritans and the Separatists who became known later in history as the Pilgrims, but it's probably worth pointing out that they didn't found the United States or even make up a overly significant portion of early immigrants to the United States.

That they did is one of the myths current Evangelicals like to propagate as they claim to be religiously descended from them. They are not, by the way.

Interestingly enough, by the time of the Declaration of Independence, the colonies that became the United States had become relatively secular, much less formally religious than almost anywhere in Europe, when measured by church attendance and by financial support of churches. Lots of people didn't go and didn't tithe.

This is another fact modern Evangelicals like to cover up, as they claim a mythical religious founding of the United States that just isn't true.

They draw a straight line from the arrival of the Pilgrims, who became so unpopular among other new Americans that their religious beliefs and practices died out, to the founders, many of whom could not fairly be described as Christians, most of whom based their ideas of government on thoroughly secular philosophies rather than Christian values.