Actually: everyone who is not a Mormon apostate or a murderer or an adulterer is ‘already saved’ in LDS theology–to either the telestial, terrestrial, or celestial kingdom. This follows the Second Coming of Christ and the Milenium. However, the rest of us languish in Spirit Prison unless and until we accept the Gospel from a visiting Mormon–and unless and until someone performs the ‘ordinances’ for us, including sealing us to a spouse. Only those of us who achieve the ‘celestial’ kingdom can experience eternal progression.
Actually I should not use the phrase “us”: I am an apostate–a former Latter-Day Saint. So I get to spend eternity in Outer Darkness with Lucifer/Satan, the demons, and unrepentant adulterers (unless I repent in this life in time to atone for my unfaithfullness). Murderers get it really tough: they are deemed to have committed the ‘blasphemy of the Holy Spirit’. They must not only fully repent but must also consent to be executed in a manner which causes their blood to spill onto the ground in atonement for taking a human life without just cause. This is the only way they get to escape eternity in ‘Outer Darkness.’
Of course since ‘eternity’ and ‘endless’ are not measures of time, but are proper names for God (Doctrine and Covenants 19:10-12, Moses 1:3, 7:35)–there’s no real telling how long I would actually have to spend in “Outer Darkness”. The topic has come up in Priesthood meetings a couple of times, and once in a Fireside (informal gathering at someone’s home). Some LDS toy with Origen’s idea that in the end, even Satan will be redeemed . . . .
Mormonism places great stress upon SELF-RELIANCE, but some things are beyond what one can do alone. This life is the proper time to hear the gospel and receive the ordiancnes of the LDS Church for oneself. If one perishes without doing this, one usually gets a ‘second chance’ (except as noted a moment ago) while in Spirit Prison. It will not be ‘as easy’ to accept the Gospel in Spirit Prison, and one will have specially-difficult obstacles to overcome. Those who choose in this life to accept the Gospel may get quite a head start on you in their own eternal progression. BUT conversions after this life ARE possible in LDS teaching, hence the performance of proxy baptisms, temple sealings, and so forth for as many deceased folks as the LDS can garner names for.