Separate of Church and State as most people believe it to be isn't actually in the Constitution nor any of the amendments.
Wikipedia has a well written good overview:
https://en.wikipedia.org/wiki/Separation_of_church_and_state_in_the_United_States
Here's a primary excerpt.
The first amendment to the US Constitution states "Congress shall make no law respecting an establishment of religion, or prohibiting the free exercise thereof." The two parts, known as the "establishment clause" and the "free exercise clause" respectively, form the textual basis for the Supreme Court's interpretations of the "separation of church and state" doctrine.
[40] Three central concepts were derived from the 1st Amendment which became America's doctrine for church-state separation: no coercion in religious matters, no expectation to support a religion against one's will, and religious liberty encompasses all religions. In sum, citizens are free to embrace or reject a faith, and support for religion—financial or physical—must be voluntary, and all religions are equal in the eyes of the law with no special preference or favoritism.
The First Congress' deliberations show that its understanding of the separation of church and state differed sharply from that of their contemporaries in Europe. As the 19th-century historian
Philip Schaff observed: