Here are some statements by Joseph Smith that appeared in 1842 in the church magazine Time and Seasons:
"Mr. Stephens' great developments of antiquities are made bare to the eyes of all the people by reading the history of the Nephites in the Book of Mormon. They lived about the narrow neck of land, which now embraces Central America, with all the cities that can be found. Read the destruction of cities at the crucifixion of Christ, pages 459-60. Who could have dreamed that twelve years would have developed such incontrovertible testimony to the Book of Mormon? surely the Lord worketh and none can hinder."
"Since our 'Extract' was published from Mr. Stephens' 'Incidents of Travel,' &c., we have found another important fact relating to the truth of the Book of Mormon. Central America, or Guatimala [Guatemala], is situated north of the Isthmus of Darien and once embraced several hundred miles of territory from north to south.-The city of Zarahemla, burnt at the crucifixion of the Savior, and rebuilt afterwards, stood upon this land as will be seen from the following words in the book of Alma:-'And now it was only the distance of a day and half's journey for a Nephite, on the line Bountiful, and the land Desolation, from the east to the west sea; and thus the land of Nephi, and the land of Zarahemla was nearly surrounded by water: there being a small neck of land between the land northward and the land southward.' [See Book of Mormon 3d edition, page 280-81.]
"It is certainly a good thing for the excellency and veracity, of the divine authenticity of the Book of Mormon, that the ruins of Zarahemla have been found where the Nephites left them: and that a large stone with engravings upon it as Mosiah said; and a 'large round stone, with the sides sculptured in hieroglyphics,' as Mr. Stephens has published, is also among the left remembrances of the, (to him,) lost and unknown. We are not going to declare positively that the ruins of Quirigua are those of Zarahemla, but when the land and the stones, and the books tell the story so plain, we are of opinion, that it would require more proof than the Jews could bring to prove the disciples stole the body of Jesus from the tomb, to prove that the ruins of the city in question, are not one of those referred to in the Book of Mormon."
If these statements sound a little overenthusiastic, they at least show that Joseph Smith believed that archaeology would eventually prove that the Book of Mormon is true.