You are correct -- man did not exist before Genesis 2:7. The section this verse is in, is in "the generations of the earth" section, not the first chapter creation of the earth section. In other words, Genesis 1 provides the overview of all God created, while Genesis 2 provides details in reference to mankind (the generations).
What is man?
Body -- from dust, returns to dust
Spirit -- life force from God, returns to God at death. The word for "breath" in Genesis 2:7 is "rauch" which is used all over the OT for spirit. This is not Holy Spirit, but the spirit of man that knows nothing about God (see I Corinthians 2:11). This is what gives man life itself.
I Corinthians 2:11 -- for what man knoweth the things of a man, save the spirit of man which is in him? even so the things of God knoweth no man, but the Spirit of God.
The fusion of these produces the living being (the person him or herself, a living soul).
What was created in Genesis 1 regarding man and woman?
The Hebrew is indefinite (as to time) on these creation verses regarding man. For example...
Genesis 1:27,28 -- And creating is the Elohim humanity in His image. In the image of the Elohim He creates it. Male and female He creates them. 28 And blessing them is the Elohim. (Concordant version).
Instead of a one-time act, it is a process God started that will not be complete until Christ finishes his redemptive work.
To support this I provide the following.
Christ is the image of God (Colossians 1:15). If man was already in the image of God, Christ would not have had to sacrifice himself. If Adam was fully in the image of God, he couldn't have sinned let alone transgress a direct command from God.
Genesis 5:3 -- And Adam lived an hundred and thirty years, and begat a son in his own likeness, after his image; and called his name Seth
The image of man is not the image of God.
- Romans 8:29 -- For whom He foreknew, He also predestined to be conformed to the image of His Son, that He might be the firstborn among many brethren.
Since believers have the need to conform their thinking and actions to Christ, who is the image of God, they necessarily are not in that image now.
- II Corinthians 3:7 -- But we all, with open face beholding as in a glass the glory of the Lord, are changed into the same image from glory to glory, even as by the Spirit of the Lord.
God began the process of creating man in Genesis 1:27. Note this highly informing verse. God says this after Adam and Eve's disobedience.
- Genesis 3:22 -- And saying is Yahweh Elohim, "Behold! The human becomes as one of us, knowing good and evil.
Knowing good and evil is related to being in God's likeness. Considering this, and the truth that the Lamb was slain from the foundation of the earth (Revelation 13:18), we see man's so-called fall was really the first step in becoming like God.
Eventually, God will be All in all, every person reflecting His image fully, even as Christ does now.