Paul paints a gloomy picture of the situation of the Gentiles before the coming of Jesus: "without hope and without God in the world." At the same time, he is realistic about the Jews, the Chosen People: just as much as the Gentiles, Israel needed to be reconciled with God through the cross of Jesus.
Strikingly, this passage affirms that Jesus in himself is our peace. This is a further example of a general principle which is elaborated more clearly in the seven sayings in John's Gospel, where Jesus affirms that he is the light of the world etc. The general principle is that Jesus is what he brings. Jesus brings light to a world in darkness and so he can affirm: "I am the light of the world."
He brings us truth and so he affirms "I am the truth." He gave us a peace which the world cannot give and so he himself is our peace and now he "dwells among us, our hope of glory" (Col 1:27).
Paul affirms that "through him we both have access in one Spirit to the Father" and so reminds us that Jesus affirmed "I am the way" and taught us that we can only come to the Father through him.
Lord Jesus, dwell in our hearts as our peace and our hope.