The First Amendment states, "Congress shall make no law respecting an establishment of religion,"
The phrase prohibits Congress, and therefore the Federal government, from making any laws regarding religion. That right was left to the individual states, many of which had been settled by those fleeing religious persecution, and those states had established religions at the time of the revolution. The founders therefore meant to prohibit the federal government from meddling in religion.
The concept of "separation of church and state" is not found, nor implied in the First Amendment. It is the result of years of twisted interpretation by the judiciary.
The matter of the insertion of "under God" into the Pledge of Allegiance by Congress was not, nor was it intended to be, establishment of a religion; it was merely the continuation of our founders and American society's traditional belief in the existence of a Supreme Being, as evidenced by the Declaration of Independence.