The scripture you cite is only Adam naming Eve. Is this supposed to be your evidence of the bible claiming Adam and Eve as the first humans? That's rather nonsensical.
So, I will answer my own question for you since you are reluctant to participate. The answer is "It does not". That being said you have to allow for the possibility that both evolution as we currently understand it, and the creation of Adam and Eve could both be true.
Here is how.
Genesis 1:26-28
26 And God said, Let us make man in our image, after our likeness: and let them have dominion over the fish of the sea, and over the fowl of the air, and over the cattle, and over all the earth, and over every creeping thing that creepeth upon the earth.
27 So God created man in his own image, in the image of God created he him; male and female created he them.
28 And God blessed them, and God said unto them, Be fruitful, and multiply, and replenish the earth, and subdue it: and have dominion over the fish of the sea, and over the fowl of the air, and over every living thing that moveth upon the earth.
These "humans" created here eventually become us. Our evolutionary ancestors as we know them. The mitochondrial "Adam and Eve". These people, or us, are known as the 6th day creations.
Biblical Adam and Eve were not created until much much later. Here Adam is created after the 7th day when God rested.
Genesis 2:7
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.
Then later Eve in Genesis 2:21-22
21 And the Lord God caused a deep sleep to fall upon Adam, and he slept: and he took one of his ribs, and closed up the flesh instead thereof;
22 And the rib, which the Lord God had taken from man, made he a woman, and brought her unto the man.
You see Adam and Eve were created for a specific reason, but that reason was not to populate the Earth. It was already populated by the 6th day creations in Genesis 1.
Later on after Adam and Eve were expelled from Eden. There is more evidence of the 6th day creations as Cain conceived a child with one of them.
Genesis 4:16 for Cain
16 And Cain went out from the presence of the Lord, and dwelt in the land of Nod, on the east of Eden.
17 And Cain knew his wife; and she conceived, and bare Enoch: and he builded a city, and called the name of the city, after the name of his son, Enoch.
Here Adam and Eve had another child named Seth who also conceived a child with our ancestors to continue the bloodline you can follow the genealogy on your own from there.
Genesis 4:25
25 And Adam knew his wife again; and she bare a son, and called his name Seth: For God, said she, hath appointed me another seed instead of Abel, whom Cain slew.
26 And to Seth, to him also there was born a son; and he called his name Enos: then began men to call upon the name of the Lord.
Anyways this is what the Bible actually claims.