Adam did not exist before God made him from the dust of the ground. And it was after Adam was formed that he became a living soul due to God breathing into him the breath of life.
7 And Jehovah God formed man of the dust of the ground, and breathed into his nostrils the breath of life; and man became a living soul.
God gave unto Adam the breath of life.
Cross Reference:
1 Corinthians 15:45
So it is written: "The first man Adam became a living being;" the last Adam a life-giving spirit.
The last Adam was Jesus. Through the first Adam sin entered the world. Through the blood sacrifice of the last Adam, Jesus, death through sin was overcome. Jesus took the sins of the world upon Himself on the cross. The last blood sacrifice for sin.
See also this scripture.
"The body shall return to the dust from
whence God took it. And the breath that He put into the body to turn man into a living soul, returns to Him. Its the breath that returns to God and NOT a soul. Soul is the combination of God 's breath and the dust he took from the earth."
The Book of Ecclesiastes chapter 12 (King James Version)
Our physical death is what is known as the first death. The second death is what happens when someone dies in their sins, they are not saved, and are then cast into outer darkness. Or, into Hell, as some teach also.