In LDS doctrine we believe that the intelligence (consciousness of man) is eternal. It has always existed.
Doctrine and Covenant 93:29
29 Man was also in the beginning with God. Intelligence, or the light of truth, was not created or made, neither indeed can be.
God then took our intelligences and through the process of procreation our intelligences entered into a spirit body which we believe is made of matter. Thus our spirits are the literal offspring of God.
Acts 17:28-29
28 For in him we live, and move, and have our being; as certain also of your own poets have said, For we are also his offspring.
29 Forasmuch then as we are the offspring of God, we ought not to think that the Godhead is like unto gold, or silver, or stone, graven by art and man’s device.
Doctrine and Covenants 131:7-8
7 There is no such thing as immaterial matter. All spirit is matter, but it is more fine or pure, and can only be discerned by purer eyes;
8 We cannot see it; but when our bodies are purified we shall see that it is all matter.
We then were allowed to take on a physical body of flesh and bones by being born into this world. Our physical bodies will die but our spirits are eternal in nature and continue to live and have consciousness. Jesus, after his death, went among the spirits of the dead and preached his gospel.
1 Peter 3:18-20
18 For Christ also hath once suffered for sins, the just for the unjust, that he might bring us to God, being put to death in the flesh, but quickened by the Spirit:
19 By which also he went and preached unto the spirits in prison;
20 Which sometime were disobedient, when once the longsuffering of God waited in the days of Noah, while the ark was a preparing, wherein few, that is, eight souls were saved by water.
1 Peter 4:6
6 For for this cause was the gospel preached also to them that are dead, that they might be judged according to men in the flesh, but live according to God in the spirit.
Eventually our spirits will be reunited with an immortal resurrected body of flesh and bones to exist eternally.
1 Corinthians 15:20-22
20 But now is Christ risen from the dead, and become the firstfruits of them that slept.
21 For since by man came death, by man came also the resurrection of the dead.
22 For as in Adam all die, even so in Christ shall all be made alive.
Basically we have always has consciousness and we have existed as just intelligences, then spirits, then with physical bodies, then back to spirits, and finally we will all be resurrected to live eternally in immortal bodies of flesh and bones.