We are saved and justified when we receive and believe in Jesus Christ, and we are saved by grace through faith (which is the faith of Jesus Christ, a gift of God). This can be seen from the following scriptures:
John 1:12 But as many as received Him, to them He gave the right to become children of God, to those who believe in His name.
Mark 16:16 He that believeth and is baptized shall be saved; but he that believeth not shall be damned.
Heb 10:39 But we are not of them who draw back unto perdition; but of them that believe to the saving of the soul.
Acts 16:31 And they said, Believe on the Lord Jesus Christ, and thou shalt be saved, and thy house.
Eph 2:8 For by grace are ye saved through faith; and that not of yourselves: it is the gift of God:
Gal 2:16. Knowing that a man is not justified by the works of the law but by faith in Jesus Christ, even we have believed in Christ Jesus, that we might be justified by faith in Christ and not by the works of the law; for by the works of the law no flesh shall be justified.
Gal 3:24 Wherefore the law was our schoolmaster to bring us unto Christ, that we might be justified by faith.
Phil 3:9 And be found in him, not having mine own righteousness, which is of the law, but that which is through the faith of Christ, the righteousness which is of God by faith:
Rom 3:26 To demonstrate at the present time His righteousness, that He might be just and the justifier of the one who has faith in Jesus.
Yes Jesus died for the sins of the world (1 John 2:2, John 1:29), but this does not mean and the Bible nowehere says that everyone was saved when Jesus died on the cross. The true Biblical gospel is that we need to receive and believe in Jesus Christ to be saved, but the idea that everyone was saved when Jesus died on the cross leads to the false gospel that we just need to believe that we are already saved. If you believe this you will believe that no repentance from sin is needed – it is pointless to repent and turn from sin if you are already saved and not a sinner.