When did knowledge of Christ's sacrifice become necessary for salvation?

I think Richard's answer is basically right but allow me to simplify it.

The way in which people have been saved has always been faith in God to forgive their sins and accept them. Take Romans 4:16 (NIV):

16 Therefore, the promise comes by faith, so that it may be by grace and may be guaranteed to all Abraham’s offspring—not only to those who are of the law but also to those who have the faith of Abraham. He is the father of us all.

As has been stated, in the OT, people sacrificed animals and were forgiven their sins not because they sacrificed an animal, but because they trusted in God to forgive them. Even though Christ hadn't yet died, by trusting in God, they were nevertheless allowed to share in Christ's redemptive work. See Hebrews 9:25-26 (NIV):

²⁵Nor did he enter heaven to offer himself again and again, the way the high priest enters the Most Holy Place every year with blood that is not his own. ²⁶Otherwise Christ would have had to suffer many times since the creation of the world. But he has appeared once for all at the culmination of the ages to do away with sin by the sacrifice of himself.

So Christ died just once for everyone. Christians are saved in the exact same way - faith in God now, means that Christ's death is effective for us too.

I think this solves your basic question - when did the change-over occur? There was no change-over - there were simply people who trusted in the God of the Bible and accepted the message of Christ as soon as they heard it. Jews like Simeon and Anna (Luke 2: 25 - 28), who got to see the baby Jesus, died as faithful Jews and I suspect the same must be true for all Jews who died waiting for Jesus (even if, unknown to them, Jesus had died some time ago without their hearing about it). Being saved as a Jew under the OT wouldn't have suddenly have made you unsaved the moment Jesus died.

Don't get me wrong, I'm not saying Jews today are saved if they haven't heard the Gospel. I'm just saying that for this period of transition, there were true believers of God who, being saved, never got to hear about Jesus' death before their died. Jews today aren't in the same situation, being fully saved and then having the object of faith change. We don't believe a Jew can be saved today without accepting Christ and so whether out of ignorance or rebellion, rejection of Jesus by ancient or modern Jews would show they weren't saved at all (and so my explanation above doesn't apply to them).

Does this help?

Unfortunately, the assumptions that you (quite usefully) stated, are where the problem lies. If you notice, you have phrased salvation as being man-dependant. In other words: "man must [hear, accept, have faith]", that means that man, in one way or another, plays a part in His own salvation, however minimal or trivial we might want to say this part is.

From Genesis to Revelation, we have God correcting this mindset, always reminding man that it is He that is sovereign, not man, and that it is God that saves, and man does not help. We confuse passages that talk about man's responsibility to believe, repent and do good as if they were talking about man's ability to believe, repent and do good.

Faith and repentance are both good works, and salvation is not by works, that no one should boast (Ephesians 2:8-9). Salvation is entirely the work of God, with no help from man. I realize that this introduces the concept of predestination and calvinism, and an enormous tangent, so I will leave most of that to another question. But in summary:

He begins the work,

Ephesians 1:4 just as He chose us in Him before the foundation of the world, that we should be holy and without blame before Him in love, 5 having predestined us to adoption as sons by Jesus Christ to Himself, according to the good pleasure of His will, 

He completes the work,

Philippians 1:6 being confident of this very thing, that He who has begun a good work in you will complete it until the day of Jesus Christ; 

and does not leave it unfinished,

John 6:37 All that the Father gives Me will come to Me, and the one who comes to Me I will by no means cast out.

John 6:39 This is the will of the Father who sent Me, that of all He has given Me I should lose nothing, but should raise it up at the last day. 

leaving nothing to chance. (Notice that the Father does the giving first before there any comes to Christ). Christ came to save that which was lost, and He leaves the 99 that are safe to rescue the one that is lost (Luke 15:14, Matthew 18:12). We are lost, not Him. He seeks and He finds.. it is not us who seek and find. So faith is a fruit of this salvation (Galatians 5:22-23), it is not a precursor. So, if God wanted to save certain people who died 5 minutes after the crucifixion, nothing can stop Him from doing so, even their lack of knowledge.

In the Old Testament (or, more precisely, pre-crucifixion times) all men were saved by the mercy of God, manifested as faith in that mercy:

Psalm 41:4 I said, "Have mercy on me, LORD; heal me, for I have sinned against you."

Abraham knew that God would provide the necessary sacrifice, and trusted Him, Paul knew that God had provided the necessary sacrifice and trusted Him, but both were chosen by God before they trusted or believed. Jesus' sacrifice transcends time, which is why He is called in Revelation 13:8 "the Lamb slain from the foundation of the world". It is a retroactive sacrifice that applies to all recipients of God's mercy. Knowledge of Christ's sacrifice is not necessary (as a prerequisite) for salvation, but it is a necessary fruit of salvation.

So, to answer your question, "When did knowledge of Christ's sacrifice become necessary for salvation?" As a prerequisite? Never. As a fruit? As soon as you believed the Gospel. Our knowledge cannot save us, only Christ can.

To answer your question sufficiently, we must come to an understanding of when was the redemptive work of Christ finished.

Currently, many people hold that the redemptive work of Christ was His crucifixion. However, that is only one aspect of the redemptive work of Christ. Classical Christian thought since Augustine, and then Aquinas, and down through the ages has held that it was through the LIFE, DEATH, and RESURRECTION of Jesus that the redemptive work of Christ was finished and not merely through the death of Christ.

Martin Luther, who was one of the strongest supporters of being a "theologian of the cross," (see the Heidelberg Disputation for more on that theology) had a incredibly solid place in his faith for the death of Christ. But for Luther, the empty tomb was the other side of the bloodied cross.

However, to focus on the crucifixion of Christ is to ignore or overlook His life lived in perfect love and the resurrection where God vindicated Jesus. Plus, we must remember that no one had faith in Jesus when He was crucified, everyone abandoned Him assuming that the Jesus movement was wrong. The disciples were gathered behind locked doors in fear when Jesus was crucified, it wasn't until the resurrection that they realized something completely else was going on.

With that being said, the "moment" when people had to start having faith in the "already accomplished reconciliation of the world" might be more accurately applied to when Jesus was resurrected (and arguably ascended too) than merely to the crucifixion of Jesus.

I hope this helps!

Pre-Christianity Salvation

The concept of "salvation" before Christ was not the same concept as we see today. The idea of salvation back then was that God would come and save us from whatever affliction we were dealing with. God brought salvation from the Egyptians; He brought salvation from the giants that controlled Canaan; He brought salvation from lions and from being thrown in a fire.

So, the idea that "salvation" before Christ was brought from the hope of "future redemptive work" is very much invalid. "Salvation" before Christ was brought from following God and obeying his commands.

For illustrative purposes:

Deuteronomy 28:1 (NIV)
If you fully obey the LORD your God and carefully follow all his commands I give you today, the LORD your God will set you high above all the nations on earth.

(a secular source, a non-secular source)

Pre-Christianity Remission of Sins

However, in the context of Christianity, if we say "salvation", we mean that Christ has saved us from the bondage of sin. When a Christian says "I am saved", he means that God has forgiven his sin and that he's been freed from that bondage. The debt has been paid; the sin is forgiven.

The concept of remission of Sins pre-Christ was that of animal sacrifice. The sacrifice of the animal was performed for the atonement of sins. (See Leviticus 4 and Leviticus 16.)

To show that sins were forgiven:

Leviticus 16:30 (NIV)
because on this day atonement will be made for you, to cleanse you. Then, before the LORD, you will be clean from all your sins.

Once the Isrealites were scattered from the promised land, the animal sacrifices stopped and prayers from the forgiveness of sins began.

I won't go into that too deep. But here's a post on Judaism.SE that explains why they are not required to sacrifice animals: Why don't Jews sacrifice animals anymore?

The point, though, is that the Jews (pre-Jesus and currently) are not expecting future redemption to be forgiven of sins. They are (rightly so) expecting their sins to be forgiven at the time when they ask for forgiveness and truly repent.

The Salvation of Jesus

The sacrifice of Jesus on the cross has brought about a new type of salvation: salvation from sins. He has provided us a way to gain access to God directly; he has become our mediator, our savior, and our redeemer.

When people hear of Jesus, his story, his resurrection, and the forgiveness of sins that we have through his sacrifice, it is at that point that they become culpable for believing or disbelieving his sacrifice.

Prior to hearing of Jesus and learning of his sacrifice and his grace and mercy, people are still under the old ways and the old rules. (See also What happens to people who have never heard about Jesus?)

To answer your question:

The requirement was never "faith in future redemptive work". The requirement was sacrifice of atonement and repentance. This requirement is still around today, but the atonement was the perfect atonement made on the cross. Prior to learning about Jesus, we must make atonement in other ways. After learning about Jesus, we can accept his amazing gift of his sacrifice as the perfect atonement.

The burden lies on the heart, not on the timing. It's learning about Jesus that changes the "salvation" (forgiveness) from atonement through animal sacrifice to atonement through messianic sacrifice.

Summary

The sacrifice of Jesus completely changed the concepts of "salvation" and forgiveness of sins. His sacrifice allows people to be forgiven of their sins without the sacrifice of animals. He has become the perfect sacrifice for us.

The requirement for forgiveness was never "faith in future redemptive work". The requirement has always been faith in God and following his laws. (Remember, Jesus didn't come to abolish the law, but to fulfill it.)

It is the point of learning of Jesus and accepting him as the Messiah that allows us to turn from other atonement to the perfect atonement. Once we accept Jesus, we can rest on his perfect sacrifice.