When was God first associated with America as an integral part of the nation itself?

“In God We Trust” was put on US coinage in 1864 . The lyrics to My Country ‘Tis of Thee were written in 1834, which included a linking of God to the US in the last stanza. I do not know when “In God We Trust” became the de facto national anthem but I know it was in the 1800’s, the Star Spangled Banner was later adopted as the official national anthem.

Is this the earliest linking of God to America and, if the 1800’s were the first such linking, were there any other significant incidents to make America considered a “Christian nation” in that century?