What is the Biblical evidence that Jesus did exist prior to his conception in Mary's womb by the Holy Spirit?
James E. Talmage treats the ante-mortal existence of Christ in his book "Jesus the Christ". For a fuller treatment see chapter 2 of this book. Here are a few instances he adduces to demonstrate that Jesus did exist prior to His mortal conception:
In the opening lines of the Gospel book written by John the apostle, we read: “In the beginning was the Word, and the Word was with God, and the Word was God. The same was in the beginning with God. All things were made by him; and without him was not anything made that was made. … And the Word was made flesh, and dwelt among us, (and we beheld his glory, the glory as of the only begotten of the Father,) full of grace and truth.” The passage is simple, precise and unambiguous. We may reasonably give to the phrase “In the beginning” the same meaning as attaches thereto in the first line of Genesis; and such signification must indicate a time antecedent to the earliest stages of human existence upon the earth. That the Word is Jesus Christ, who was with the Father in that beginning and who was Himself invested with the powers and rank of Godship, and that He came into the world and dwelt among men, are definitely affirmed.
When, on a certain occasion, the Jews in the synagog disputed among themselves and murmured because of their failure to understand aright His doctrine concerning Himself, especially as touching His relationship with the Father, Jesus said unto them: “For I came down from heaven, not to do mine own will, but the will of him that sent me.” … Not a few of the disciples failed to comprehend His teachings; and their complaints drew from Him these words: “Doth this offend you? What and if ye shall see the Son of man ascend up where he was before?” (John 6:38, 61–62)
Also, in the Intercessory Prayer:
And now, O Father, glorify thou me with thine own self with the glory which I had with thee before the world was. (John 17:5)
There are a few more scriptures Talmage uses; I hope this helps!
The biblical evidence is in John's Gospel. Mark's Gospel portrays Jesus as human, adopted by God at his baptism, while the Gospels of Matthew and Luke portray him as the Son of God from his conception:-
David Rhoads, Joanna Dewey and Donald Michie say, in Mark as Story, page 104:
In Mark, Jesus is the son of God, but not by virtue of a special birth or a divine nature. He became God's son at his baptism, when God anoints him with the holy spirit. In Mark, Jesus is neither God nor a divine being, but a human, a son of humanity, who has been given great authority by God.
Keith F. Nickle says (Preaching the Gospel of Luke, page 15):
For Luke, Jesus was the Son of God from his conception. (There is no evidence that Luke knew of a view that affirmed preexistence which became incarnate as the Son of God, as we find in the Gospel of John.)
The biblical evidence that Jesus was actually pre-existing and divine is found throughout John's Gospel, but particularly at John 1:1-2, 14:
John 1:1-2: In the beginning was the Word, and the Word was with God, and the Word was God. The same was in the beginning with God.
John 1:14: And the Word was made flesh, and dwelt among us, (and we beheld his glory, the glory as of the only begotten of the Father,) full of grace and truth.
AND THOU, BETHLEHEM Ephrata, art a little one among the thousands of Juda: out of thee shall he come forth unto me that is to be the ruler in Israel: and his going forth is from the beginning, from the days of eternity. (Micah 5:2, Douay-Rheims)
This shows us the ruler having the eternal properties seen only in God.