In the OT, atonement was accomplished by the substitutionary death of animals regularly and often in the place of the human sinner.
In the NT, atonement is accomplished by substitutionary death of the Son of God, ONE time for all mankind.
The Wages of sin is death, but the gift of God is eternal life. The Gift is Jesus who died in our stead. Whosoever believeth in Him should not perish but have everlasting life.
Does Jesus' atonement mean that the sins of the world are forgiven? No, but the wage for those sins is paid in our stead, that is, we are not held liable for the sins that Jesus death paid for. That is not forgiveness, it is atonement, expiation and the first stage of reconciliation. This happened approximately 2000 years ago.
The second stage of reconciliation is individual Belief in Jesus, the Lamb of God. This happens afresh for each human who comes to belief in the Christ.
After belief unto faith in Jesus, then comes the believer's obedience to the Christ. As one becomes familiar with the Word of God, the Holy Spirit then influences the human spirit by convicting one of the sins in the one's life thus compelling one to confess those sins. It is this confession of one's sins that initiates forgiveness from the one who atoned for the sins of all mankind.