Romans says God demonstrates his love by Christ dying for sinners. The point is not that people made themselves lovable first, but that God's love is shown while people are weak, ungodly, and in need of reconciliation.
Romans 5:6-11 expands the peace and hope described at the start of the chapter. Paul grounds confidence in the cross: if God loved and reconciled enemies through Christ's death, believers can trust his saving purpose.
This makes God's love concrete. Romans points to the death of Christ as the public proof of grace for people who could not rescue themselves.
should not detach this verse from justification and reconciliation. God's love in Romans 5 is covenant-restoring action, not only sentiment.
Original wording based on Romans 5:6-11.