To the primary question -
Why don’t Unitarians believe that Jesus Christ pre-existed before incarnation?
Because there is no scripture saying he did... Only in the mind of God who planned what His creation would need... a saviour.
There is no verse that states Jesus pre-existed his conception and birth through Mary. Nor is there any verse that speaks of an 'incarnation' or, 'God became a man'. Many think there is, but this is based on a traditional view of scripture which does not align exactly with the text. If the incarnation was so important to reveal the beginning of Jesus, we would be reading about it in the bible - but we do not. The Gospels DO tell us all we need to know.
From Gen 3 on, we're told of a man who would come to defeat evil. He did come ~2000 yrs ago when the 'logos' become flesh - a man who could be tempted and die. God is incapable of dying! God cannot become a man and die - else he would not be God anymore. How does God stop being God to the point that he could die? This doesn't make any sense not is there scripture that expressed this, Phil 2:6-7 included.
Certainly the NT is consistent about Jesus being a man only. If he is a man only, a sinless man, how could he possibly pre-exist?
The idea that the logos IS God and therefore a 'person' from which Jesus originated in a misreading of the text and is addressed here.
No Jew would ever think John was speaking of a God apart from the Father - the one God.
1 Pet 1:20 For He was foreknown before the foundation of the world, but has appeared in these last times for the sake of you
Jesus was 'foreknown' by God before the world was made - why is he so if he already existed?
There are texts that might be read to show a pre-existing identity that became Jesus, but they are not Jesus yet - not before his birth.
Unitarians believe in the God revealed in the bible as one God, who alone created through His word, His command, wisdom, plan... logos.
They believe in His son, who is NOT God, but the result of God's intervention with His spirit upon Mary to miraculously conceive a male child.
Heb 1:1-2 God, after He spoke long ago to the fathers in the prophets... in these last days has spoken to us in His Son, whom He appointed heir of all things, through whom also He made the world’
No, he didn't make the 'world', he made the 'ages'. Translators who insist on 'world' or worse, 'universe', are deviating from the text to support their case. How could Jesus make the world - he was only born ~2000 yrs ago. "Last days" "appointed heir" - doesn't sound very pre-existing... certainly not as Jesus!
Jesus always has a God - even once ascended Rev 3. It's stated so many times... How can Jesus be God is he has a God - just like we do, just like Mary did?
John 20:17… I am ascending to your Father and my Father, to my God and your God’
Regarding John 14:6
Jesus answered, "I am the way and the truth and the life. No one comes to the Father except through me. (NIV)
During OT no one comes to the Father at all unless He calls them for a task and they then represent others in their office as leader (Moses, Aaron) or King or prophet, priest. The OT was not a time of being with God in the way that we may through His spirit and Christ as high priest. Sacrifices needed to made all the time, as the people were 'ceremonially' unclean. In Jesus, we are clean, sanctified, justified etc. through one perfect sacrifice for all people for all time. Heb 2:9-11, Heb 5:7-10, especially Heb 10
Jesus sacrifice occurred ~2000 yrs ago, but it reaches back through time to cover all men who inherited sin from Adam.
So yes, NO ONE comes to the Father except via Jesus - no one can have their sin removed except by HIS sacrifice - not even David or Moses or Elijah. They had an understanding of the 'one to come' which they wrote about but did not fully grasp the magnitude of who Jesus was and what he would do.
Acts 4:12 Neither is there salvation in any other: for there is none other name under heaven given among men, whereby we must be saved.
We cannot confuse a prophecy - a promise of something or someone to come at a later date, with a present reality in that day of prophecy. David looked forward, as did Abraham, to the day when Jesus would come. John 8:56