Several boks have been put forth as America's First Novel."
Orooniko, 1688, published at the time of the author's experiences in the West Indies. English author, so not really applicable.

William H. Brown, 1791, The Power of Sympathy.
Susanna Rowson, 1791 (1794 US), Charlotte Temple.
H. W. Foster, 1797, The Coquette.
Charles B. Brown, 1799, Wieland.
Washington Irving, 1809, A History of New York, by D. Knickerbocker.
William Williams, 1815, The Journal of Penrose, Seaman. (Set in Nicaragua)
James Fennimore Cooper, 1826, Leatherstocking Tales, The Last of the Mohicans.