Question: If Adam wasn’t the first man why does Luke’s genealogy trace Christ’s line all the way back to Adam?
Answer: The fact that Luke highlights the genealogical line all the way back to Adam shows us that Adam most probably wasn’t the first man. Otherwise there’s no need to highlight the line all the way back to Adam. If Adam is the progenitor of the whole human race then there’s no need to mention Christ’s line goes all the way back to Adam because everyone’s line goes all the way back to Adam, so why mention it in the first place? Matthew’s genealogy of Jesus doesn’t go any further back than Abraham. Luke could have followed Matthew’s example because scholars tell us that Matthew's Gospel was written before Luke’s Gospel. Going all the way to Adam seems superfluous if everyone’s genealogical line ends with Adam. But if Adam was chosen as a representative human and God breathed into him in some special way, and made a woman from his rib so that the generating of this couple would lead eventually to Christ’s birth, then Luke would have every reason to mention the line all the way back to Adam. Paul in Romans 9:3-5 explains that to "his race, the people of Israel... belongs the human ancestry of Christ... traced through the fathers." i.e. Son of David, Son of Abraham, Son of Adam, all of whom were fathers in the line to Christ. Adam means "man" - Christ is the Son of man.
Isaiah points out that it is Israel's ancestry that comes from Adam, "Your first forefather sinned" (Isa 43:27). A little later Isaiah mentions that it is Israel who were established from ancient times. "I established my ancient people" (Isa 44:7).
Furthermore, Genesis 4:1 states that "Adam lay with his wife Eve and she conceived and gave birth to Cain." Why mention that "Adam" lay with his wife if there were no other men around? Genesis wants us to know that it was Adam who was the father of Cain, not another man. The signs are throughout Genesis if we look - that is why we get the feel that there were other people around at the time of Adam and Eve. Genesis for Ordinary People provides more examples.