All I've talked about are these verses:
Psalm 2:7
I will declare the decree: the Lord hath said unto me, Thou art my Son; this dayhave I begotten thee.
Acts 13:33
God hath fulfilled the same unto us their children, in that he hath raised up Jesus again; as it is also written in the second psalm, Thou art my Son, this day have Ibegotten thee.
Hebrews 1:5
For unto which of the angels said he at any time, Thou art my Son, this day have Ibegotten thee? And again, I will be to him a Father, and he shall be to me a Son?
All of these verses are talking about the same thing. The Psalm is prophetic and Acts is the fulfillment.
Psalm 2:7
I will declare the decree: the Lord hath said unto me, Thou art my Son; this dayhave I begotten thee.
Acts 13:33
God hath fulfilled the same unto us their children, in that he hath raised up Jesus again; as it is also written in the second psalm, Thou art my Son, this day have Ibegotten thee.
Hebrews 1:5
For unto which of the angels said he at any time, Thou art my Son, this day have Ibegotten thee? And again, I will be to him a Father, and he shall be to me a Son?
All of these verses are talking about the same thing. The Psalm is prophetic and Acts is the fulfillment.
And, you do realise that the context of Ps 2:7 and Heb 1:5 is also not referring to the physical conception and birth of Jesus Christ as an infant to Mary do you not? At the very least it cannot just be referring to His physical conception and birth because the context makes it very clear that the reference is to an eternal being.
God is not the father of Jesus Christ in the sense that any man on earth is the father of his son.
When God is spoken of as Father, and the father of Jesus Christ, it is not a reference to sexual reproduction, however, it is clearly meant to indicate that the Son proceeds from the Father, that He finds His being from the Father.
You have correctly deduced that both God the Father and Jesus Christ are eternal. They are both separate beings.
Yet, they are also one, because they are part of the same Godhead.
To emphasise: the word begotten used in these verses does have a primary meaning related to physical descent (sexual reproduction), yet the object of the verb, is also clearly spoken of in eternal terms. So, the word "begotten" here, cannot merely refer to the physical creation of a descendant, since, by definition, that excludes the eternality of the object of the verb, in this case the Son, Jesus Christ.
The fact that Jesus Christ is (in human terms) referred to as a descendant of the Father is not a reference to His conception and birth as the son of Mary. He was already the Son of God for eternity. This is an anthropomorphism, an attempt to explain in human terms, a much larger concept that Jesus Christ, the Son of God, while most emphatically a separate being, is yet indistinguishably and indissolubly God in the same way as the Father and that those attributes flow from the Father. In a way that it is not physical (through DNA) Jesus Christ inherits His divinity from the Father.
Remember that you are the one that has highlighted the apparent contradiction of an eternal being, Jesus Christ, having a father/son relationship with God the Father that would require, by necessity, the son being a created being, if the literal meaning of the word "begotten", was applied. Psalms chapter 2 makes it clear that the Son is being referred to in an eternal sense, so any meaning applied to the verse must take that into account. The first chapter of Hebrews certainly makes the eternality (in the context of emphasising His divinity) of Jesus Christ crystal clear, the quotation of Ps 2:7 notwithstanding.
For Jesus Christ to be the Son of God, it means that He must, in some way have descended, and have an inheritance, from the Father. Clearly this cannot be mediated in terms of DNA and a physical creative event. How, exactly, this occurs, between two eternal spiritual beings is not exactly explained in Scripture. Instead, apparently contradictory juxtapositions are used to communicate the relationship between God the Father and the Son of God, Jesus Christ!