Salvation without belief in Christ? Let’s see what else Paul has to say.
Rom 1:20-25
Ever since the creation of the world his invisible nature, namely, his eternal power and deity, has been clearly perceived in the things that have been made. So they are without excuse; for although they knew God they did not honor him as God or give thanks to him, but they became futile in their thinking and their senseless minds were darkened. Claiming to be wise, they became fools, and exchanged the glory of the immortal God for images resembling mortal man or birds or animals or reptiles. Therefore God gave them up in the lusts of their hearts to impurity, to the dishonoring of their bodies among themselves, because they exchanged the truth about God for a lie and worshiped and served the creature rather than the Creator, who is blessed for ever! Amen.
Rom 2:14-16
When Gentiles who have not the law do by nature what the law requires, they are a law to themselves, even though they do not have the law. They show that what the law requires is written on their hearts, while their conscience also bears witness and their conflicting thoughts accuse or perhaps excuse them on that day when, according to my gospel, God judges the secrets of men by Christ Jesus.
These two passages give light to everything Paul says about “salvation for non-believers” and to the substance of the Church’s teaching on the matter.
Please note that the first passage indicates that no man has an excuse for not believing in God. Therefore, those that fully reject God’s grace and refuse to believe in God will not be saved. They apparently have “no excuse.”
The second passage makes it clear that the gentiles may not have had the OT law available to them, and it also makes it clear that this ignorance applies to ignorance of Christ. We know that this extends to ignorance of Jesus because of Paul’s reference to “that day when…God judges the secrets of men by Christ Jesus.” “That day” is a reference to the end of time and the final judgment. Those that are ignorant of Jesus and have, therefore, no way of coming to Christ “might” still be saved. Only God will judge their final disposition of heart, mind, and soul.
This is the essence of the Church’s teaching. It in no way negates the truth that we are only saved through our Lord Jesus Christ. It merely means that the mercy of God may apply the redemptive merits of Jesus to those that are innocently ignorant of Christ. In the end, God in His infinite wisdom, justice, and mercy will decide who will and who will not enter His divine presence.
I hope this helps.