This is how I understand it:
There was sin in the world BEFORE Adam.
How do I know? Because the "Serpent" was on the world and he was already a liar, a false teacher, a thief and a murderer. Death passed upon men because a LAW was given and they disobeyed, namely "Thou shalt not EAT" of the tree of knowledge of good and evil. When Adam disobeyed that law, death passed upon him. Read it for yourself......
12Wherefore, as by one man sin entered into the world, and death by sin; and so death passed upon all men, for that all have sinned: 13(For until the law sin was in the world: but sin is not imputed when there is no law. 14Nevertheless death reigned from Adam to Moses, even over them that had not sinned after the similitude of Adam's transgression, who is the figure of him that was to come.
We are "shapen in iniquity"