Most of what I have to say is pretty obvious....but I never let that keep me from talking! ;-)
In trying to understand why Adam seems to be absent from the Old Testament, outside of Genesis, I realized a very obvious thing....Israel didn't care about theological issues that encompassed the entire world. They weren't trying to find a way to make everything fit together, to understand what God was going to do with everyone else on earth.
That wasn't their concern.
Their primary goal was to uphold their particular chosen tribe in what they saw as the ways of God. Because their religious narrative involved God choosing Abraham and blessing his physical descendants, or at least those descended from Isaac, they had no reason to worry themselves about pagans, Gentiles, or outsiders.
This shows up in their slavery laws and in their wars with surrounding nations.
God had made his choice. The other nations were only receiving whatever judgement they deserved. Israel was God's path to blessing or cursing the nations according to many of their Scriptures.
As a result, tracing all of humanity back to a literal Adam would have been relatively meaningless for their theological perspective.
What Paul does with Adam is actually quite ingenious. By bringing Adam into the picture and making his comparison to Jesus, Paul declares a new creation that resets humanity back at an equal starting place. Suddenly, being Jewish holds no special privileges. Anyone can be accepted by God and equally receive his favor.
In Romans, Paul equivocates, speculating that God's promises to Israel which have been extended to all, might be even greater if Israel, as a whole, accepted Jesus as their Messiah. Even Paul is not willing to completely close the door on Israelites. So, while developing a theology that is wide open to pagans and Gentiles, he still hopes that Israel will have a special place with God.
However, the point is that Paul uses the figure of Adam in a way that permits everyone to participate in the Kingdom of God.
This is always Paul's mission--to bring the Gentiles in, to declare that all are welcome.
Paul uses the same technique in Galatians when he turns the idea of Abraham's seed completely on its head and gives it a novel interpretation:
7 Understand, then, that those who have faith are children of Abraham. 8 Scripture foresaw that God would justify the Gentiles by faith, and announced the gospel in advance to Abraham: “All nations will be blessed through you.” 9 So those who rely on faith are blessed along with Abraham, the man of faith.
10 For all who rely on the works of the law are under a curse, as it is written: “Cursed is everyone who does not continue to do everything written in the Book of the Law.” 11 Clearly no one who relies on the law is justified before God, because “the righteous will live by faith.”12 The law is not based on faith; on the contrary, it says, “The person who does these things will live by them.” 13 Christ redeemed us from the curse of the law by becoming a curse for us, for it is written: “Cursed is everyone who is hung on a pole.” 14 He redeemed us in order that the blessing given to Abraham might come to the Gentiles through Christ Jesus, so that by faith we might receive the promise of the Spirit.
15 Brothers and sisters, let me take an example from everyday life. Just as no one can set aside or add to a human covenant that has been duly established, so it is in this case. 16 The promises were spoken to Abraham and to his seed. Scripture does not say “and to seeds,” meaning many people, but “and to your seed,” meaning one person, who is Christ.
He's doing the same thing he did with Adam, taking a figure from the Scriptures and using it to persuade others that God really did want everyone on board.
I'm left with the feeling that I usually have for Paul, annoyance that he so boldly moves forward in new directions, with what I would think are less than pure exegetical moves, and admiration that he could find a way to make it work and admiration for the general thrust of trying to open the doors as wide as possible for everyone.