This is a pretty heavy subject. However, from what I understand, God made man's body, then breathed life into his nostrils and he became a living soul. This is the only creature that becomes a living soul.
Soul there simply is a figure of speech that means a person or human or a living thing...it is not the same meaning as the soul within a person like our spirit.
Living soul is also used of animals:
Gen 2:7 And the LORD God formed man of the dust of the ground, and breathed into his nostrils the breath of life; and man became a
living soul.
Living soul, khah'ee nephesh
Gen 1:21 And God created great whales, and every
living creature that moveth, which the waters brought forth abundantly, after their kind, and every winged fowl after his kind: and God saw that it was good.
Living creature is the same Hebrew words, khah'ee nephesh
H5315
נפשׁ
nephesh
neh'-fesh
From H5314; properly a breathing creature, that is, animal or (abstractly) vitality; used very widely in a literal, accommodated or figurative sense (bodily or mental): - any, appetite, beast, body, breath, creature, X dead (-ly), desire, X [dis-] contented, X fish, ghost, + greedy, he, heart (-y), (hath, X jeopardy of) life (X in jeopardy), lust, man, me, mind, mortality, one, own, person, pleasure, (her-, him-, my-, thy-) self, them (your) -selves, + slay, soul, + tablet, they, thing, (X she) will, X would have it.
Soul may have been an ok translation hundreds of years ago but it is misleading and causing doctrinal errors and false teachings today.
This is a far better translation for today's English:
(GW) Then the LORD God formed the man from the dust of the earth and blew the breath of life into his nostrils. The man became a living being.
(ISV) So the LORD God formed the man from the dust of the ground, breathed life into his lungs, and the man became a living being.
(TLV) Then Adonai Elohim formed the man out of the dust from the ground and He breathed into his nostrils a breath of life—so the man became a living being.