By claiming that the church is "the only true church on the earth" one presupposes not only that all other churches must contain lesser truth, but that there must needs be one church that is more true than any other. Perhaps it is this assumption itself that is erroneous.
Most religious traditions claim to be either the one true church, or more true than other, lesser belief systems. There are hundreds of millions of people who lay claim to "knowing" that their belief system is the correct one, be they LDS, Evangelical Christian, Moslem, Jewish, etc. The problem is, this "knowledge" is mutually contradictory. If the Baptists are correct, then the Catholics must not be; if there is not God but Allah and Mohammed is His prophet, then the Hindus must be idol worshipping heathens, as taught by the Koran.
To support their own particular claim, members of the LDS church point to the prophetic calling of Joseph Smith. His works included the translation of the Book of Mormon and the restoration of the priesthood after centuries of apostasy. One would expect, had God indeed stood behind this new religion, that the truthfulness of LDS claims would soon be self-evident. Yet church growth has not even outstripped that of other Christian offshoots from the same time period. The Jehovah's Witnesses and Seventh Day Adventists began at roughly the same time period, make similar claims, and can boast of similar growth. None of them have yet to make serious inroads in the approximately two billion Christians on the planet, however, and none approach the rapid growth of the Pentecostal movement from zero to 350,000,000 adherents in only a century.
In the end, it is likely that there is so much confusion regarding the truth claims of various religions, because God has not chosen to reveal His purpose in a way that is unambiguous. Perhaps He has called different leaders from different cultures, giving each of them a different path. Perhaps He has yet to appear in direct form. Perhaps, as atheists and agnostics will speculate, He does not exist at all.
Alas, it is difficult to answer the above conjecture with any degree of certainty. Perhaps these questions will never be answered. And perhaps it doesn't matter.
I believe the most important goal should be to carve one's own path, a path as authentic and tolerant as we can manage. An alternative would be to take whatever path was given in childhood and seek to improve it as you go. But it is important to recognize that not everyone will choose the same path that you have and that's okay too.