This exhibition demonstrates that many of the colonies that in 1776 became the United States of America were settled by men and women of deep religious convictions who in the seventeenth century crossed the Atlantic Ocean to practice their faith freely.
While this is true, it did not mean that the First Amendment was inevitable. Many of these people came across so that they could practice their religion freely, but they didn't necessarily believe in religious freedom for all. For example, take a look at the early history of the Massachusetts Bay and Plimoth Plantations Colony.
The original Pilgrims came over because a lack of religious freedom forced them to leave England. But they then moved to the Netherlands, not America. In the Netherlands, they were in fact free to practice their version of Christianity. However, because there was religious freedom of a sort in the Netherlands, their children were being exposed to alternate religious beliefs, and were becoming (from the Pilgrim parents' point of view) corrupted in their faith. So the Pilgrims left the Netherlands and came to America to establish a colony where their faith would be the only one, where they would be free to practice their faith, but no one else would.
Congregationalism was established as the state religion. All had to attend services and give money and other support to it, regardless of their personal beliefs. Non-conformance was punishable by fines, imprisonment, tarring and feathering, exile, and ultimately death. Some Quakers paid the full measure of those punishments. It's a long way from that to the First Amendment. I wonder if this web site will talk about that.