The first time the Bible mentions it is in Genesis 2.7: "and the humans became living souls." It doesn't say that humans were given souls, or that they began to have souls, but that they became souls. It's not trying to comment on monism (humans are a unity), bipartite (humans are bodies and souls), or tripartite (body, soul, spirit) theology. What it does imply is that "soul" became the characteristic of his being. Nephesh (נֶפֶשׁ) is used in a variety of ways, but often of the whole person, and occasionally the way that whole person connects to God (the soul).

Some commentators warn that we're not to make more of this than what it says. Harris, Archer, & Waltke, in their lexicon, say: "the substantive must not be taken in the metaphysical, theological sense in which we tend to use the term 'soul' today. Man is here being associated with the other creatures as sharing the passionate experience of life and is not being defined as distinct from them. It is true, however, that the source of the nepesh of animals is the ground, whereas the source of the nepesh of Adam is God."

Still, this verse is the first mention and seems to indicate when humans became "soulish."

Those of you who (like the Pope) understand evolution and don’t believe the earth is a few thousand years old: when did human beings begin to have a soul?