It fits quite comfortably within his doctrine of cosmic redemption in Jesus Christ alone. Jesus

is the head of the body, the church. He is the beginning, the firstborn from the dead, that in everything he might be preeminent. For in him all the fullness of God was pleased to dwell, and through him to reconcile to himself all things, whether on earth or in heaven, making peace by the blood of his cross. And you, who once were alienated and hostile in mind, doing evil deeds, he has now reconciled in his body of flesh by his death, in order to present you holy and blameless and above reproach before him, if indeed you continue in the faith, stable and steadfast, not shifting from the hope of the gospel that you heard, which has been proclaimed in all creation under heaven (Colossians 1.18-23).

Jesus has reconciled all things and therefore he has reconciled you also if you believe the Gospel being preached to all creation.

Is this unclear? Is it questionable from anything else in the Pauline writings?