How do we know God's forgiveness is real?

In 2 Samuel 12, after being confronted with his sins, King David acknowledges his wrongdoing, confessing to Nathan, 'I have sinned against the Lord.' Nathan then reassures David, stating, 'The Lord also hath put away thy sin; thou shalt not die.' This moment exemplifies the grace of God, whereby repentance leads to immediate forgiveness. The text illustrates that when we earnestly confess our sins to God, He is faithful to forgive us, demonstrating His love and mercy despite the gravity of our offenses. Furthermore, it indicates that forgiveness costs something; for David, it foreshadowed the ultimate sacrifice of Jesus Christ, who would take on the sins of the world, allowing for full reconciliation with God.