Why does God offer hope to sinners?
Hope is extended because of all that God has done, not human deserving. Although people are born sinners in Adam, God justifies freely, without a cause, declaring the believing sinner just as if he had never sinned. This justification is a judicial act of God and a promise.
Les explains that people are not sinners merely because they break the law; they are sinners because they are sons of Adam, born basically as sinners. That would leave the situation hopeless, but because of all that God has done, it is not hopeless. The promise is that believers are justified freely, without a cause. To justify someone is to declare them just as if nothing had ever happened. In the scriptural realm, justification is God's judicial act whereby He declares the sinner who believes just as if he had never sinned. God did not get backed into a corner and justify people because they deserved it; rather, He justifies freely without a cause even though they do not deserve it, when they believe.