If Adam isn’t real, then neither is ‘original sin.’
If original sin isn’t real, then there’s no need for a Savior.
If there’s no need for a Savior, then Jesus is a liar.
To be honest, I’m not sure that these premises are true.
Adam doesn’t have to be “historically real” for there to be original sin. I’ll try and put it this way. If Adam figuratively represents the first humans, then the moral of the story is that all humans share in a common sin: an inability to trust God. I think that is true whether we have historical first parents or not. Our parents were sinners. We’re sinners. Our children will be sinners. We all choose to participate in that original sin when we place ourselves above God. That’s what sin is.
In regards to the second premise, Jews don’t believe in original sin as Christians do, yet the Pharisaic tradition holds that they needed a Messiah to rescue them from the bonds of sin. Our original sin is wiped away by Baptism. Yet we still sin after Baptism. Even if we reject the concept of original sin (which I emphasize that I am not arguing for), we would still need to be saved from our other sins.
For the third premise, this one is a little more interesting. While my approach is not likely what you were implying, I still think that it is a good theological question. Let’s suppose that humans never sinned and do not sin. Would Jesus still have entered the world? St. Thomas Aquinas, among others, argued yes. Humans are sensible creatures, meaning that we best see the world through our physical senses. Since we are made for communion with God (and others), it seems fitting that God would come into the world physically to enter into relationship. Now, the Incarnation has different theological causes, and of course sin was one reason that it is necessary, but think about God in the garden. It seems like God was walking among man and there was a harmony that was lost after the fall. Just food for thought.
Just as a retroactive disclaimer, my comment is not to argue whether Adam has any historical basis, but my comment is intended to raise a challenge to the argument that you proposed.