Captain Symmes had not been the first to suggest this idea in 1818, but he found especial notice, and some of his followers, such as James McBridge, the pioneer, published a book of his theory, Symmes's theory of concentric spheres : demonstrating that the earth is hollow, habitable within, and widely open about the poles (1826), and pushed for explorations to find such a passage.
Uncle Dale Broadhurst, as always, has the scoop on how these musings turn up in early and later Mormon history. Ezra Booth had claimed (in Eber D. Howe, Mormonism Unvailed, 1834, p.127) that Joseph Smith Jr felt the Northern tribes were in the polar regions, separated by ice and mountains from the rest of the world; and the revelation that was printed in the Evening and Morning Star (May 1833) soon thereafter, writes:
And the Lord even the Savior shall stand in the midst of his people, and shall reign over all flesh. And they who are in the north countries shall come in remembrance before the Lord, and their prophets shall hear his voice, and shall no longer stay themselves, and they shall smite the rocks, and the ice shall flow down at their presence. [= D&C 133:26]Which may not be as clear as we would like it to be, but the north and the rocks and the ice are all there, at any rate.
Dale Broadhurst also argues that the fact that the July 1832 edition of the Evening and Morning Star can cite another article that refers to the theory of Capt. Symmes without any explanations indicates that Symmes was considered common knowledge at this point.
That the Symmes theory was well known in all religious circles of the time is best highlighted by the mention that the Rev. McCalla made in his closing arguments on pedobaptism against Alexander Campbell, where McCalla eschewed discussing the issue again "until an opponent would come from the regions discovered by Captain Simmes", as reported in (Richardson 1870, 2:86).
James McBride was involved in questions of Indian Monuments in other ways as well. He had made drawings that found their way into Squier and Davis' landmark 1848 Ancient Monuments of the Mississippi Valley, with which the Smithsonian inaugurated their Contributions to Knowledge series. Even though a landmark in its description, that work was still dominated by the assumption that a different race than the then-living Indians had built the monuments.
In addition to relying on other's artwork, Squier and Davis used travel descriptions to identify what to map, for example, Thaddeus Harris' The journal of a tour into the territory northwest of the Alleghany Mountains ; made in the spring of the year 1803 : with a geographical and historical account of the state of Ohio ; illustrated with original maps and views, printed in Boston in 1805. Or the descriptions of H.M. Brackenridge's Views of Louisiana : containing geographical, statistical and historical notices of that vast and important portion of America (1817) printed in Baltimore.
They also relied on Caleb Atwater's 1819 memoire in the Archaeologia Americana (Vol I, 1820), entitled Description of the Antiquities discovered in the State of Ohio and other Western States (Uncle Dale Broadhurst has excerpts of Atwater's memoire, too, of course). [Interestingly enough, in that very volume of the Archaeologia Americana, pp.325ff and then pp.333ff, there are discussions on the Indians coming from Asia, mostly due to similarities of physical features. Of course, as some of the authors point out, some people were trying to have the Indians come from Plato's Atlantis (p.340), e.g. Mathieu of Nantes RCK] They may have used Secretary Joseph Moulton and John Yates' History of the state of New-York : including its aboriginal and colonial annals, 1824, as well.
Harris' account was reprinted in volume 3 of Reuben G. Thwaites twenty-plus volume collection, Early Western Travels 1748-1846, printed in Cleveland, Ohio, in 1906. Reuben G. Thwaites was an American historian and friend of Frederick Jackson Turner, who would travel the Ohio River for "color" in the way that 19th century military historians like Delbrück would walk battle fields.