This is the exact conclusion I have reached as well, after years of studying Genesis.
Over the last few years I have to say that I have become less than convinced that the Bible intends, anywhere, to portray the origin of sin. We don’t know why, for example, the snake is in the garden trying to corrupt Eve and thus Adam also. Rebellion began before Adam. That sin enters the human line with an original pair simply doesn’t seem to be the point in either the Old or New Testaments. On the other hand, the Bible clearly portrays the universal impact of sin and the places the blame firmly on mankind as a species, as communities, and as individuals. Rebellion is the point. We are formed to need God, to be in fellowship with God. But this relationship, like our other relationships, is broken. Broken by us, not by God. Broken time and time again.