According to Scripture the spirit of man is created, formed or made.
“For you formed my inward parts; you knitted me together in my mother's womb. I praise you, for I am fearfully and wonderfully made. Wonderful are your works; my soul knows it very well.”
The spirit of man is in the inward parts of man.
“But it is the spirit inside man, the breath of the Almighty, that makes him understand.”
There are other passages with reference to the spirit of man and it’s properties but if it isn’t clear enough that the spirit is made consider,
“The oracle of the word of the Lord concerning Israel: Thus declares the Lord, who stretched out the heavens and founded the earth and formed the spirit of man within him:”
The Hebrew word יצר used here is used elsewhere to show a formation, like a potter using clay to form a vessel. God therefore may very well have used the raw material of His own Breath but the spirit of man in its raw form is non-functional inside a biological machine until God forms the spirit.
Though the spirit of man is made/formed from God’s Breath they are distinct and separate. Man’s spirit is not equivalent to the Spirit of God.
“For who knows a person's thoughts except the spirit of that person, which is in him? So also no one comprehends the thoughts of God except the Spirit of God.”
1 Corinthians 2:11
This verse has OT connection as a side note
“The spirit of man is the lamp of the Lord, searching all his innermost parts.”
Therefore given it is created it is not preexisting as is God Himself
“For by him all things were created, in heaven and on earth, visible and invisible, whether thrones or dominions or rulers or authorities—all things were created through him and for him.”
And should anyone question or require further clarification on this point about creation or formation
“By faith we understand that the universe was created by the word of God, so that what is seen was not made out of things that are visible.”
Universe in its classic sense meaning anything and everything in existence physical or otherwise. These were made of things that are invisible.
And the spirit is invisible made of the invisible but coupled with a biological machine can manifest itself
“See my hands and my feet, that it is I myself. Touch me, and see. For a spirit does not have flesh and bones as you see that I have."”
This is also pertinent to the incarnation because Jesus was given a body (Heb 10:5) but His spirit was placed inside of a body. His spirit was preexisting. So Mary did not give birth to “God”, she did not create God, nor was she required to be sinless because the body was given to Jesus and His Spirit placed inside it. She gave birth to a biological machine into which the spirit of Jesus was placed. Hence He was fully human, he had a human BODY and fully God, His Spirit was the same (minus his glory which He removed voluntarily).
Humans however do not get preexisting spirits or recycled spirits. They yes, are expected to exist in some point in time after Creation in the future because they are in a register called the book of life written prior to Creation but until they are made they don’t exist. There are also spirits that were never intended to exist and were never written in the book of life, a hybrid being/beast (Genesis 6). Much like a blueprint is not a house until it is constructed, so our spirits are not formed until conception but exists in a register.
“Your eyes saw my unformed substance; in your book were written, every one of them, the days that were formed for me, when as yet there was none of them.”