God's last acts of Creation was that God formed man and woman. First God created man's body. Everything was in place but it was lifeless. Next God, started man's heart, and lungs to function and man came alive. God was the source of life, although the material man was made of was lifeless matter of the earth it only became a "living being" when God put life into it. God breathed in man's nostrils the breath of life. The word breath is used in various ways in Scripture, Generally it means "spirit" which this seems to be what is meant here. God gave man the "spirit of life."
The word "soul" can be translated as "being." It is not referencing man's spiritual nature, but of his being alive. The word is used also in reference to animals, yet we know animals do not have a living spiritual soul as does man. Animals were not being created in God's image, having intelligence, will and emotion. Animals were created for the benefit of man as was all of Creation. (Genesis 1:28) Animals live by instinct rather than by their intelligence directed by their will. God programmed animals to function instinctively as they do. There is no Scripture that suggests animals will go to heaven. They will be apart of the Millennium, but are not mentioned in the New Heavens and Earth.
Theistic evolution that accepts the hypothesis of the evolution of man directed by God can not find support for their false ideas in the Genesis account of the Creation of man. The Biblical narrative states man was made personally by God from the dust of he earth. It does not say man came from an evolution of the family of primates (monkeys, apes, chimpanzees and etc). It states man was first created and then energized or made a living being. Man did not come from living matter but from inert material which was formed by special Creation of God and then given life.