Are there any Bible verses that confirm this theology?
On Biblical support for every soul being created by God, as opposed to every soul pre-existing without God:
7 Then the Lord God formed a man from the dust of the ground and breathed into his nostrils the breath of life, and the man became a living being.
Genesis 2:7 NIV
This verse is almost identical in the King James, which Joseph Smith was using.
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.
Genesis 2:7 KJV
Adam wasn't a "living being" or a "living soul" until God breathed in "the breath of life." God didn't create a human body and wait for a pre-existing soul to drop in. God didn't pick out a pre-existing soul. God created Adam's soul.
In John Gill's commentary we are told that the "breath of God" was required for Adam to become a "thinking, reasoning" creature.
<< And breathed into his nostrils the breath of life;
which in that way entered into his body, and quickened it, which before was a lifeless lump of clay, though beautifully shapen: it is in the plural number, the "breath of lives"
F12, including the vegetative, sensitive, and rational life of man.
And this was produced not with his body, as the souls of brutes were, and was produced by the breath of God, as theirs were not; nor theirs out of the earth, as his body was: and these two different productions show the different nature of the soul and body of man, the one is material and mortal, the other immaterial and immortal:
and man became a living soul;
or a living man, not only capable of performing the functions of the animal life, of eating, drinking, walking but of thinking, reasoning, and discoursing as a rational creature. >>
Link
Genesis 2:7 - Commentary & Verse Meaning - Bible
Later in the Old Testament we find:
This is what God the Lord says—
the Creator of the heavens, who stretches them out,
who spreads out the earth with all that springs from it,
who gives breath to its people,
and life to those who walk on it:
Isaiah 43:5 NIV
John Gill's commentary on this verse:
<< he that giveth breath unto the people upon it;
as he did to man at first, he breathed into him the breath of life, and as he gives to all since ... >>
Link
Isaiah 42:5 - Commentary & Verse Meaning - Bible
Breath comes up again in Acts, when Paul is preaching in Athens.
25 And he is not served by human hands, as if he needed anything. Rather, he himself gives everyone life and breath and everything else.
Acts 17:25 NIV
From John Gill's commentary on this verse:
<< seeing he giveth to all life and breath;
or
"the breath of life", as the Ethiopic version renders it; this God breathed into man at first, and he became a living soul; and every animate creature, everyone that has life and breath, have them from God; he gives them to them, and continues them ... >>
Link
Acts 17:25 - Commentary & Verse Meaning - Bible
I hope this helps.