What might be taken from this passage?
Genesis 3:22-24 (KJV)
22 And the LORD God said, Behold, the man is become as one of us, to know good and evil: and now, lest he put forth his hand, and take also of the tree of life, and eat, and live for ever:
23 Therefore the LORD God sent him forth from the garden of Eden, to till the ground from whence he was taken.
24 So he drove out the man; and he placed at the east of the garden of Eden Cherubims, and a flaming sword which turned every way, to keep the way of the tree of life.
It appears to me Adam and Eve were not immortal, but were denied that state of being by separation from the Tree of Life.
Adam had his initial state of being as a lump of clay in God's hands on the sixth day of creation. That's why some preaching a funeral point out we are from dust, and to dust we return, referring to Gen 3:19, used of the whole of the human lineage, except for those who remain alive when the Lord returns.
As for their holiness status, that appears to have been conditional upon keeping that one commandment not to eat of the tree of knowledge of good and evil. One commandment! They broke it and paid a huge price, dragging all their offspring into troubles.