Put on the new self, created after the likeness of God in true righteousness and holiness. Paul describes not a goal but an invitation to put on what already exists. The new self IS created. You put it ON.
Sonship means: you are remade in God's image. Righteousness and holiness are not achievements but characteristics of your new being. You do not become holy through doing, you ARE holy through being.
Closeness to God is natural because you are created in his image. Distance is the abnormal thing.