The phrase "separation of church and state" is not in the First Amendment. You won't find that phrase anywhere in our Constitution. The phrase came from a letter from President Thomas Jefferson to the Danbury Baptist Association. The Association had written to Jefferson out of concern that the government would interfere with the inalienable right to worship. President Jefferson responded on January 1, 1802 and assured the Association that the government would not establish a state religion nor would the government interfere in their right to worship.
The First Amendment to the US Constitution simply says "Congress shall make no law respecting an establishment of religion, or prohibiting the free exercise thereof."