There seems to be no Biblical evidence that Jesus is
eternally begotten. "This day I have begotten you" means there was a day/ a time. when Jesus was begotten.
Rev. 1 says Jesus was first-begotten out from the dead.
Ps. 2 links "This day I have begotten you" to the time Jesus was set as King on God's holy hill in heaven.
Heb. 1 links "This day I have begotten you" to "after he purged our sins", at the same time as he graduated from being "a little lower than the angels" to "by inheritance obtaining a better name than angels", before "He sat down on the right hand of God".
It looks to me that the Son was begotten when He rose from the dead was glorified with His new incorruptible body. (Zec. 3, John 20:17, Luke 24:36-43).
Psalm 2:6 Yet have
I set my king upon my holy hill of Zion.
7 I will declare the decree: the Lord hath said unto me,
Thou art my Son; this day have I begotten thee.
8 Ask of me, and I shall give thee the heathen for thine inheritance, and the uttermost parts of the earth for thy possession.
9 Thou shalt break them with a rod of iron; thou shalt dash them in pieces like a potter's vessel.
Heb. 1:1 God, who at sundry times and in divers manners spoke in time past to the fathers by the prophets, 2has in these last days spoken to us by his Son, whom he has appointed heir of all things, by whom also he made the worlds; 3who being the brightness of his glory, and the express image of his person, and upholding all things by the word of his power,
when he had by himself purged our sins, sat down on the right hand of the Majesty on high; 4being made so much better than the angels, as he hath by inheritance obtained a more excellent name than they. 5For unto which of the angels said he at any time,
You are my Son,
This day have I begotten you?
And again,
I will be to him a Father,
And he shall be to me a Son?
6 And again, when he brings in the firstbegotten into the world, he says, And let all the angels of God worship him. 7 And of the angels he says,
Who makes his angels spirits,
And his ministers a flame of fire.
8 But to the Son he says,
Your throne, O God, is for ever and ever:
A sceptre of righteousness is the sceptre of your kingdom.
9You have loved righteousness, and hated iniquity;
Therefore God, even your God, has anointed you
With the oil of gladness above your fellows.
Rev. 1:
4 John to the seven churches which are in Asia: Grace be unto you, and peace, from him which is, and which was, and which is to come; and from the seven Spirits which are before his throne;
5 And from Jesus Christ, who is the faithful witness, and
the first begotten of the dead, and the prince of the kings of the earth. Unto him that loved us, and washed us from our sins in his own blood,
6 And hath made us kings and priests unto God and his Father; to him be glory and dominion for ever and ever. Amen.