The first Adam and the Last Adam had the same exact purpose--to fill the earth with the image and likeness of God. If you want to know what the Last Adam is going to do, look at what the first Adam was supposed to do. They were two people with the same divine destiny. God did not need His image and likeness in the realm of His pre-creation existence. It was already there. He wants it in the created realm; that is why He created Adam in His image and according to His likeness in the first place. Christ's sacrifice on the cross was a son-for-son exchange and redemptive reversal to restore the image, likeness, and light of God back to man in the created realm where He wants it revealed.
Redemption is not about going to heaven one day; in fact, the believer is already seated in heavenly places in Christ Jesus. Redemption is about the restoration of the created realm through the Lamb of God, who shed His blood to create it and shed His blood to redeem it. As believers, we have been born of incorruptible seed that is the Word of God to look like and reveal God in and to the creation.