If you think Jesus only became Jesus when he was conceived in the flesh of the virgin Mary you're basically flirting with Arianism, that's where you've gone wrong. Jesus was around before even Mary's ancestor Abraham. Jesus Christ the same yesterday, and today, and forever. Jesus is the only eternally begotten Son of God.
The person who became named in the first century "Jesus of Nazareth" has always existed. I have already agreed with that.
Heb. 1:
8 But unto the Son he says Your throne, O God, is for ever and ever: a sceptre of righteousness is the sceptre of your kingdom.
9 You have loved righteousness, and hated iniquity; therefore God, even your God, has anointed you with the oil of gladness above your fellows.
10 And, You, Lord, in the beginning have laid the foundation of the earth; and the heavens are the works of Your hands:
11 They shall perish; but You remain; and they all shall wax old as does a garment;
12 And as a vesture shalt You fold them up, and they shall be changed: but You art the same, and your years shall not fail.
But we are discussing the claim that Jesus is eternally begotten. We know from scripture that He was conceived by Mary through the power of the Holy Spirit. There was a time when He was not physically in Mary's womb, and then He became physically present; so we could say He was physically begotten (caused to begin to exist physically) at the incarnation.
Luke 1:35 And the angel answered and said unto her, The Holy Ghost shall come upon thee, and the power of the Highest shall overshadow thee: therefore also that holy thing which shall be born of thee shall be called the Son of God.
And we know that He was begotten out from the dead by the power of the Holy Spirit. There was a time when He was physically dead, and His soul was present in Hades among the rest of the souls of the physically dead, and then He became physically alive and His soul .left the realm of the dead. So we could say He was begotten (He was caused to begin to exist physically alive again) out from the midst of the physically dead.
To beget means to cause something to begin to exist. There is no biblical or logical reason to claim that a Person who has always existed spiritually was caused to begin to exist (i.e. was begotten) spiritually. YOu have yet to supply any scripture that conforms that.
As for your lifting of Heb. 13:5 out of context to place Jesus of Nazareth in eternity -
5 Let your conversation be without covetousness; and be content with such things as ye have: for he hath said, I will never leave thee, nor forsake thee.
6 So that we may boldly say, The Lord is my helper, and I will not fear what man shall do unto me.
7 Remember them which have the rule over you, who have spoken unto you the word of God: whose faith follow, considering the end of their conversation.
8 Jesus Christ the same yesterday, and to day, and for ever.
I see that the author is addressing the motivations of his audience: covetousness and contentment. He reminds the audience that before ascending into heaven in 30AD, Jesus had promised never to leave nor forsake His disciples. He conclu=des from this that Jesus must be present today and able to help His disciples, therefore we need not fear what man does to us.
The author then tells the disciples that as confirmation of that promise, they should consider the lives of those who taught them the gospel, who believed Jesus promise to never leave nor forsake, and experienced Jesus' help during their walk of faith. He tells his audience to imitate their teachers in practising the same confidence in Jesus as they have. He assures them that Jesus is the same in the experience of the post-ascension disciples since 30 AD (i.e yesterday), and in the audience's lifetimes (today) and without end intomthe future (forever).
The context does not justify us taking the sense of "yesterday" back further than 30AD when Jesus made the promise: "I will never leave you nor forsake you.'