From Anstey’s Doctrinal Definitions:
This term is not found in Scripture, though the truth that it conveys most certainly is. It refers to Christ’s relationship in the Godhead as Son being that which has existed eternally. It is not referring to the eternality of His being, but to the eternality of His Sonship. Some mistakenly think that while He existed eternally as one of the Persons in the Godhead, He did not become the Son until His incarnation. This error is called “Temporal Sonship.” The following passages indicate that Christ’s sonship is eternal:

Proverbs 30:4 indicates that Christ’s Sonship not only existed before His incarnation, but it existed before the creation of the world!

Colossians 1:13-16 and Hebrews 1:1-2 state that Christ, as the Son of God, created the world, thus proving that His Sonship existed long before He came into this world as a Man.

Isaiah 9:6 and John 3:16 also indicate that Christ’s sonship existed before He came into this world. These verses state that the Son of God was “given,” and in order for something to be given, it first would have to be in existence. If not, the word “given” loses its meaning.

Many passages of Scripture (especially in John’s Gospel) attest to the fact that Christ, as the Son of God, was “sent” of the Father. Again, this shows that Christ’s Sonship had to have pre-existed His Manhood, otherwise “sent” would also lose its meaning. See Mark 12:6; John 3:17; 3:34; 4:34; 5:23-24, 30, 36, 37-38; 6:29, 38-39, 40, 44, 57; 7:16, 18, 28, 29, 33; 8:16, 18, 26, 29, 42; 9:4; 10:36; 11:42; 12:44-45, 49; 13:16, 20; 14:24; 15:21; 16:5; 17:3, 18, 21, 23, 25; 20:21; Acts 3:26; Romans 8:3; Galatians 4:4; 1 John 4:9, 10, 14.

J. N. Darby said, “If I have not Him as Son before born into the world, I lose all that the Son is. If He is only so as incarnate, you have lost all the love of the Father in sending the Son” (Collected Writings, vol. 25, p. 230-231). He also said, “‘The Father sent the Son to be the Saviour of the world.’ He did not send an idea merely. There was a living Person there who said He was sent. Nor was it merely when in this world that He was sent, for He says, ‘I came forth from the Father, and am come into the world’” (Notes and Comments, vol. 2, p. 281).

John 1:18, in reference to Christ as the Son of God, states, “which is in the bosom of the Father.” The word “is” in this verse refers to the eternal present.

John 11:27 states that Christ is “the Son of God which should come into the world.” The words, “should come” confirm that He pre-existed His Manhood.

John 16:27-28 indicates that Christ as the Son of God “came forth from the Father.” This shows that He was along side of the Father before He came into this world.

In John 17, the Lord addresses the “Father” as being the “Son.” This Father and Son relationship is alluded to all through the prayer. Twice He makes reference to something that existed between them before the foundation of the world: the “glory” that He had as Son with the Father (vs. 5), and the “love” that He as Son enjoyed from the Father (vs. 24). These two things clearly show that He was with the Father as the Son before His incarnation.

Hebrews 5:8 shows that there was a point in the Lord’s personal history when He, as “the Son,” didn’t know what it was to be obedient, having never been subjected to obedience. This, of course, was before He became a Man. This verse states that in spite of being “the Son,” when He became a Man, He had to learn obedience like every other man—only, of course, He learned it in perfection. H. Smith said, “He learned by experience what it cost to obey” (Outline of the Epistle to the Hebrews, p. 31).

1 John 1:1-2 states that Christ, “the Eternal Life,’”was “with the Father” before being “manifested” in this world. The fact that He was “with the Father” before coming into the world, shows that He was there as the Son, for “father” and “son” are co-relative terms; there cannot be a father without there being a son! Hence, He, as the Son, pre-existed His incarnation. Mr. Darby remarked, “What is called ‘The Eternal Sonship’ is a vital truth, or we lose the Father sending the Son, and the Son creating, and we have no Father if we have no Son” (Notes and Comments, vol. 2, p. 300).

Hebrews 7:3 describes the characteristics of Melchisedec’s priesthood. The inspired writer is not saying that Melchisedec didn’t have a father or a mother, but that he is introduced in Scripture (Genesis 14) without Scripture giving us any details as to his genealogy. It is not recorded who his father and mother were. The typical teaching that the Spirit of God takes from this is that Melchisedec is presented as being an eternal person with an everlasting priesthood. The writer adds, “made like unto the Son of God,” because he assumes that we all know that the Son of God is eternal.

J. N. Darby said, “The notion of Sonship in Christ only when incarnate is destructive to the very elementary joy of the Church, and abhorrent to those who have communion by the Spirit in the truth” (Collected Writings, vol. 3, p. 89). He also said, “I hold it vital to hold the Sonship before the worlds. It is the truth.”

J. G. Bellett said, “It is evident that the Son was the eternal One, the name of this eternal Son being Jesus Christ” (Bible Treasury, vol. 6, p. 57).

W. Kelly said, “Under all changes, outwardly, He abode as from eternity, the Only-begotten Son in the bosom of the Father. Hence, the Son being in this affable nearness of love, has not God only, but the Father (Lectures Introductory to the Gospels, on John 1, p. 463).

C. H. Mackintosh said, “Question the Eternal Sonship of Christ, question His deity, question His unspotted humanity, and you have opened the floodgate for a desolating tide of deadly error to rush in” (Notes of the Pentateuch, Leviticus, p. 39).

W. T. P. Wolston said, “The Father was never incarnate, and the Spirit of God was never incarnate; but the Son of God, the Word, ‘became flesh, and dwelt among us, full of grace and truth’ (John 1:14). The Eternal Son has come into this scene, humbling Himself, and becoming a Man” (Seekers For Light, p. 107).

W. Scott said, “‘Only begotten Son in the bosom of the Father’ is but once written in Scripture, and is the declaration to us of the depth and tenderness of the love in which the Son ever abode with His Father” (Bible Handbook, Old Testament, p. 72).

A. J. Pollock said, “We know from the four gospels, which of the three Persons of the Holy Trinity the Lord Jesus was, viz. the Son, the eternal Son, the Son from all eternity…to refuse to acknowledge this is the spirit of Antichrist” (The Amazing Jew, p. 45).