I think we've been down this highway before. I am led to believe that an unbeliever is one who REJECTS Christ, knowing His claim. Thus, a person who has never heard of Christ cannot be an "unbeliever" in that sense. Here is the simplest sense of who will be saved:
He that hath the Son hath life; [and] he that hath not the Son of God hath not life. 1 John 5:12
Furthermore:
And we have known and believed the love that God hath to us. God is love; and he that dwelleth in love dwelleth in God, and God in him. 1 John 4:16
I do not think the bible supports the notion that baptism confers salvation. An unbelieving atheist gets as much benefit from baptism as does a duck from a good roasting.
Baptism presumes that one is willingly accepting the notion of what it is meant to do - it is a sacrament of faith which erases sin. Being freed from sin is the formula of salvation, is it not? Baptism is for the remission of sin.
Regards
And, therefore, faith is the prior, most important, condition.
John came preaching "a baptism of repentance for the remission of sins."
The remission is from the "repentance" and not from the baptism. The baptism was the public proclamation of one's repentance.
When Peter spoke "repent and be baptized for the remission of sin" one's hermenutic should force one back to the verse that clarifies the sequence: "A baptism of 'repentance for the remission...'"
The above must be seen in light of the earlier "everyone that loveth is BORN OF GOD and knoweth God."
Following the johanine authorship, one would go to Jesus' John 3 statements about being born again. They would all conclude in the John 1 statement:
11 He came to His own, F3 and His own F4 did not receive Him. 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: 13 who were born, not of blood, nor of the will of the flesh, nor of the will of man, but of God. 14 And the Word became flesh and dwelt among us, and we beheld His glory, the glory as of the only begotten of the Father, full of grace and truth.