Since he is God since all times, did he become true human in the incarnation or he was already man before it?
No, He did not always have a human nature.
As St. John writes in the Gospel:
John 1:1,14 (DRB)
...the Word was God. ... And the Word was made flesh and dwelt among us.
St. Paul writes to the church at Philippi concerning the humility of the Son of God in becoming flesh for our salvation:
For let this mind be in you, which was also in Christ Jesus: Who being in the form of God, thought it not robbery to be equal with God: but emptied himself, taking the form of a servant, being made in the likeness of men, and in habit found as a man. He humbled himself, becoming obedient unto death, even to the death of the cross.
The Hypostatic Union
The Hypostatic Union is the doctrine that the two natures of Christ (the eternal divine, and the temporal human nature) are united in only one Person: the divine Word or Son of God.
This is why we can say "the First and the Last," and "the Lord of Glory," (1 Corinthians 2:8) that is, God, "died:"
And when I had seen him, I fell at his feet as dead. And he laid his right hand upon me, saying: Fear not. I am the First and the Last, and [am] alive, [though] was dead, and behold I am [alive] for ever and ever, and have the keys of death and of hell.
And it's why Jesus can say, though not true of His human nature, but His divine only:
John 8:58 (cf. Exodus 3:14)
... Amen, amen I say to you, before Abraham was [made], I am.
That is, simply put, anything belonging to either nature belongs to the one divine Person: the Word or Son of God. Anything predicated of either nature is predicated of the Son of God. Or, anything the Person does in either nature, He does as the Divine Person: there is no human person in Jesus Christ, only one Divine Person with two natures.
Therefore, the answer to your question
Wouldn't He have to have been human since all time, since He lives in eternity?
is no, since the natures are distinct, and are not confused nor admixed. Only the human nature of Christ died, properly speaking. Only the Divine nature of Christ created all things. But Christ (i.e. a Person) indeed did both in truth.
A Pertinent Example
A very simple doctrine which gets to the heart of the issue is the doctrine that Mary, Jesus' mother, is the mother of God (it is, fundamentally, a Christological doctrine).
In the fourth century, a heretic named Nestorius made a divison, rather than a simple distinction, between the two natures of Christ, so as to assert that we may not properly call Mary, his mother, the mother of God, but only Christ.
The heresy is summarized by the Ecumenical Second Council of Constantinople's condemnation of it in A.D. 533 (Sentence Against the Three Chapters of Nestorius):
The holy synod of Ephesus… has pronounced sentence against the heresy
of Nestorius… and all those who might later ... adopt the same
opinions as he held ... They express these falsehoods against the true
dogmas of the Church, offering worship to two Sons, trying to divide
that which cannot be divided, and introducing to both heaven and earth
the offense of the worship of man. But the sacred band of heavenly
spirits worship along with us only one Lord Jesus Christ.
Even earlier than this, and directly addressing a specific heretical product of his false Christology (that Mary was only the mother of a human nature, and not of the divine Person of God the Word), the Ecumenical Council of Ephesus (A.D. 431) issues the following anathema (Session I, Canon 1):
If anyone will not confess that the Emmanuel is very God, and that
therefore the Holy Virgin is the Mother of God [Θεοτόκος],
inasmuch as in the flesh she bore the Word of God made flesh [as it is written,
"The Word was made flesh"] let him be anathema.
What this goes to prove is that clearly Jesus was born, but this particular heretic asserted that He was not personally God who was born (the fallacious argumenting being that God was never born; yet in that He had this human nature in addition to the divine, He was born). Whereas, as the condemnation notes, Mary's Son is Immanuel (God with us), and the eternal Word of God made flesh. In this sense, she most definitely is the mother of God.