How did the supreme court apply first amendment protections to the decision of engel v. vitale?

The First Amendment to the US Constitution prohibits the establishment of a religion.

The selective incorporation doctrine has made it so the First Amendment applies to the States.

In Engel v. Vitale, the Supreme Court ruled that it was unconstitutional for a state to write an official prayer and to ask its recitation in the school, even if the recitation was voluntary.

By ruling against the State/School, the Supreme Court ensured that no State would establish a religion, protecting its citizens first amendment rights.