In the Westminster Confession of Faith and the London Baptist Confession of Faith, in chapter 2, section 3, the Confessions speak to the issue of Jesus’ “eternal begotteness” to the Father.
III. In the unity of the Godhead there be three Persons of one substance, power, and eternity: God the Father, God the Son, and God the Holy Ghost. The Father is of none, neither begotten nor proceeding; the Son is eternally begotten of the Father; the Holy Ghost eternally proceeding from the Father and the Son. (WCF 2:3)
3._____ In this divine and infinite Being there are three subsistences, the Father, the Word or Son, and Holy Spirit, of one substance, power, and eternity, each having the whole divine essence, yet the essence undivided: the Father is of none, neither begotten nor proceeding; the Son is eternally begotten of the Father; the Holy Spirit proceeding from the Father and the Son; all infinite, without beginning, therefore but one God, who is not to be divided in nature and being, but distinguished by several peculiar relative properties and personal relations; which doctrine of the Trinity is the foundation of all our communion with God, and comfortable dependence on him. (LBCF 2:3)
In this section, both Confessions take their cue from the Nicene Creed which pronounces the Son “begotten of His Father before all worlds, God of (from) God, Light of (from) Light, very God of (from) very God, begotten not made, being of one substance with the Father…”
In the Nicene formulation, the fathers stated that from all eternity, Christ has had his divine essence communicated to Him from the Father, and in this respect, He is begotten or generated from the Father, eternally (this is a non-temporal generation and the fathers equally stated that Christ was eternal and not a created creature). However, at the time of the Reformation, great theologians such as Calvin saw this differently, opting rather to proclaim that the personal Father to Son relationship is generated via the Father and communicated to the Son, BUT NOT His divine existence as YHWH, the self-existent second person of the Trinity (see the Institutes, Book 1, chapter 13). Hence, Christ is begotten in some sense, and He is eternally the Son in every sense, but, did not derive His divine existent as the second member of the Trinity from the Father, because He is after all, YHWH, the self-existent one. Rather, the Father, being first in the unity of essence, communicates the Sonship of Christ from all eternity and hence, there is a real Father to Son relationship – while the Son Himself remains fully YHWH and ontologically equal to the Father and the Spirit, sharing the same, singular essence of God. Hence, the Logos, along with all the members of the Triune Godhead are what would be called, autotheos. Meaning, all three members are self-existent as God (as there could be not existence of God outside of His Triune nature, because YHWH necessarily exists in such a fashion).
With that said, below are my notes on this most interesting topic. Please keep in mind that I would rather not have addressed this topic because to be honest, I think to some extent, this goes past Scriptural parameters and into the area of speculation. Nevertheless, the WCF does speak to the issue, so, I also did today. I hope that you find this formulation both faithful to the Scriptures and edifying.
“I would suggest, therefore, with Calvin and these American theologians, that Christians should not believe that the Father, through an eternal act of begetting in the depth of the divine being that is always continuing, is begetting the Son’s essential being as God out of his being, which act thereby “puts this second person in possession of the whole divine essence.” They should believe, rather, that the Son, with respect to his essential being, is wholly God of himself (αὐτόθεος, autotheos). They should also believe that the Son, as the second Person of the Godhead, derives his hypostatic identity as the Son from the “generated” relation “before all ages” which he sustains to God the Father, the first Person of the Godhead (what this means beyond “order” I cannot say and will not attempt to say), and that the Father precedes the Son by reason of order. This means that there is no essential subordination of the Son to the Father within the Godhead.” (Reymond, R. L. (1998). A New Systematic Theology of the Christian Faith Nashville: T. Nelson. (p 335).