How do we know that Christ truly saves sinners?

In 1 Timothy 1:15, it states that Christ Jesus came into the world to save sinners, exemplifying His intent and capability as the Savior. The historical event of His sacrificial death fulfills the divine justice required by God. The bloody battle that culminated at the cross signifies that Christ's offering satisfied God's requirements for salvation, fully redeeming His people. As the successful Savior, Jesus ensures that all He came to save will be saved, fulfilling every promise made by God regarding redemption.