The soul of the body, or the spirit, did exist before conception, yes, but we did not have physical being then.
Jesus' disciples knew that the soul existed before physical conception. Evident here:
1 And as Jesus passed by, he saw a man which was blind from his birth.
2 And his disciples asked him, saying, Master, who did sin, this man, or his parents, that he was born blind?
How could the disciples thought he might have sinned or transgressed before birth, if he did not exist, or they did not think he existed before birth?
Often, references are made to events and relationships that existed before the foundation of the world:
24 Father, I will that they also, whom thou hast given me, be with me where I am; that they may behold my glory, which thou hast given me: for thou lovedst me before the foundation of the world.
1 Peter 1:18-20
18 Forasmuch as ye know that ye were not redeemed with corruptible things, as silver and gold, from your vain conversation received by tradition from your fathers;
19 But with the precious blood of Christ, as of a lamb without blemish and without spot:
20 Who verily was foreordained before the foundation of the world, but was manifest in these last times for you ...
Paul also speaks repeatedly of a notion of foreordination, or being known and foreordained before the world ever was, for instance:
3 Blessed be the God and Father of our Lord Jesus Christ, who hath blessed us with all spiritual blessings in heavenly places in Christ:
4 According as he hath chosen us in him before the foundation of the world, that we should be holy and without blame before him in love:
Job references an occasion where all the sons of God shouted for joy when the foundations of the earth were laid.
4 Where wast thou when I laid the foundations of the earth? declare, if thou hast understanding...
7 When the morning stars sang together, and all the sons of God shouted for joy?
John the Revelator, in the Book of Revelation, saw in vision a recount of a war in heaven before Adam and Eve were placed on the earth.
7 And there was war in heaven: Michael and his angels fought against the dragon; and the dragon fought and his angels,
8 And prevailed not; neither was their place found any more in heaven.
9 And the great dragon was cast out, that old serpent, called the Devil, and Satan, which deceiveth the whole world: he was cast out into the earth, and his angels were cast out with him.
2 In hope of eternal life, which God, that cannot lie, promised before the world began;
Jude also references an organized spiritual state before this physical life.
6 And the angels which kept not their first estate, but left their own habitation, he hath reserved in everlasting chains under darkness unto the judgment of the great day.
(According to some Christian churches, this is thus our second estate, having kept our first by not following Lucifer in the war in heaven before this life.)
Just note that I do not know of many Christian faiths that actually believe or can explain the doctrine of pre-mortal existence. It is largely unrevealed to us and the Bible alone is not definitive in the description of that state. It evidently did happen, however, and I have cited only a few passages here which support that. Edit: Let me re-emphasize the general vagueness of these passages; but I would rather be comprehensive than not.