So we become complete in this fallen reality because of what He did, but don't become one with God until the end. When you say "complete", I assume you mean quickened ..renewed spirit. A righteous connection to God.
What we lack is spiritual knowledge of who we are in Christ and who He is in us. We need our minds renewed. We need to be set free from the proud and rebellious independence that hinders our walk with Lord Jesus. We are complete in Christ, but we need that to be worked out in our lives.
Watchman Nee put it something like this. God is not a chemist, dispensing remedies for various spiritual ailments. God will not give us a dose of humility to overcome pride, for example. God has one "cure" for every human condition. That is the Lord Jesus.
He's all we need, as the old song says.