If the basis of salvation is trusting in the crucifixion, how could anyone who lived prior to the crucifixion be saved by something they knew nothing about and occurred after their time?

Actually, the basis of salvation is not trusting in the crucifixion. The basis of salvation has always been, and always will be, trusting God and His promises. God is the object of our trust. His promises are the content of our trust and form the foundation for the practical day-to-day expression of our trust. The New Testament states it this way in Ephesians 2:8-9:

8 For by grace you have been saved through faith (trusting); and that not of yourselves, it is the gift of God; 9 not as a result of works, that no one should boast.

The crucifixion of Jesus happens to be the content of our faith during this current age. However, the crucifixion of Jesus has not been the content of faith in every age. Why? First, just as you stated, men were unaware of the future and so how could they know about and trust in something about which they were totally unaware. Second, God did not reveal all the information at one time. Instead He chose to reveal the information progressively, a step-at-a-time. For example, men would not know that the Messiah would die as a Guilt Offering until the time of Isaiah (700 BC) when Isaiah wrote chapter 53 of his book.

Now, when most Christians talk to people, they are talking in the present, "You have to believe in Jesus and His work on the cross to be saved." They are absolutely correct. That is correct for this age. So my first request for you to consider is what do you have to do? What do you have to do in regard to your own personal salvation today? Please do not worry about someone else who lived 4,000 years ago. You are not ignorant of the person and work of Jesus. You are living in the time when Jesus and His work on the cross is the proper object and content of faith. Please place your trust in Him.

What has been the content of faith in previous ages? That has varied from age to age because God’s revelation has been progressive. His requirements for mankind have varied through the ages. The point is that man is required to respond according to the light that he has received. That is the common denominator. For example:

• For Abraham, the basic content of his faith was the Abrahamic Covenant of Genesis 12. Abraham personally trusted God, was saved (Gen. 15:6), and expressed that trust by aligning his life with the Abrahamic Covenant. Genuine faith expresses itself in works consistent with that trust.
• After Abraham came the Mosaic Covenant. Jewish people living under the Mosaic Law personally trusted God and expressed that trust by aligning their lives with the requirements of the Law of Moses (sacrificial system, etc.).
• After the Mosaic Covenant came the current age, the age of the New Covenant described in Jeremiah 31:31. Jesus instituted the New Covenant during Passover in 30AD. People living today personally place their trust in Jesus. Rabbi Saul (Apostle Paul) said it this way, "For I delivered to you as of first importance what I also received, that Christ died for our sins according to the Scriptures, and that He was buried, and that He was raised on the third day according to the Scriptures (1 Cor. 15:3-4)." Then they express that trust by aligning their lives with the New Testament revelation.
• After the current age will come the Messianic Kingdom. People living in that time will personally trust the Divine Messianic King (Jesus) and align their lives with Kingdom Law.

The point is this: mankind is required to respond to the light that they have been given. If they respond properly—personally trusting God—then more light will be given. God wants to save them and He will lead them to the place where they will have a proper relationship to Him (salvation). We can trust in the loving nature of God. He deeply loves every soul He has created. He loves you. He wants every soul to spend eternity in fellowship with Him. He wants you to spend eternity in His presence. However, that love does not compromise His holiness. We have to come to Him on His terms. After all, He is the King of the Universe. Both His infinite love and His infinite holiness have to be satisfied without compromise.

The problem lies in the fact that very few respond properly to the truth. Very few are looking for the truth. Very few people want to admit their sinful, helpless condition and accept the grace of God. We cannot earn or merit a personal relationship with God. We are totally separate from Him, as Isaiah said:

But your iniquities have made a separation between you and your God, and your sins have hidden His face from you, so that He does not hear. Isa. 59:2

The Book of Romans tackles that question in the first three chapters. To summarize the Book of Romans (I will substantiate my comments with appropriate quotations):

Introductory Background

All men need saving because all men sin in word, thought, or deed. Romans 3 states (extensively quoting the Old Testament, which was written before the time of Jesus):

Jews and Greeks are all under sin; as it is written, "There is none righteous, not even one; there is none who understands, there is none who seeks for God; all have turned aside, together they have become useless; there is none who does good, there is not even one." ; "Their throat is an open grave, with their tongues they keep deceiving," "The poison of asps is under their lips" ; "Whose mouth is full of cursing and bitterness" ; "Their feet are swift to shed blood, destruction and misery are in their paths, and the path of peace have they not known." ; "There is no fear of God before their eyes."

In contrast to man, God is an absolutely holy being who is unrelated to sin. He is separated from sin. He tolerates sin temporarily because He is patient, loving, humble, and wants to restore the lost relationship.

Psalm 113:5--Who is like the Lord our God, Who is enthroned on high, Who humbles Himself to behold The things that are in heaven and in the earth?

Phil. 2:5--Have this attitude in yourselves which was also in Christ Jesus, who, although He existed in the form of God, did not regard equality with God a thing to be grasped, but emptied Himself, taking the form of a bond-servant, and being made in the likeness of men. And being found in appearance as a man, He humbled Himself by becoming obedient to the point of death, even death on a cross.

He will not tolerate the presence of sin forever.

Isa. 13:11--Thus I will punish the world for its evil, And the wicked for their iniquity; I will also put an end to the arrogance of the proud, And abase the haughtiness of the ruthless.

Therefore, mankind does not automatically experience a personal relationship with God. Mankind needs to be moved from the realm of darkness and sin into the realm of light and righteousness. The relationship that existed at the time of creation has to be restored. How does this happen?

The point of the book of Romans is all men are saved—all men restore their personal relationship with God—the same way our father Abraham did, by faith—by trusting God (I am going to change the word "faith" to the word "trust" because "trust" is a better translation of the idea):

Romans 4:3--For what does the Scripture say? "And Abraham trusted God, and it was reckoned to him as righteousness."

So that is the background. Romans chapters 1, 2, and 3 say essentially this.

Chapter One: All men know about God’s attributes, nature, and power from what we call "general revelation"—nature—creation. Information about God cries out to them from the world around them. The Psalmist put it this way:

Psalm 19:1-2--The heavens are telling of the glory of God; And their expanse is declaring the work of His hands. Day to day pours forth speech, And night to night reveals knowledge.

However, what do men do with this light they have been given? How should they respond? Chapter 1 says that the correct response is to honor, worship, and serve God. However, instead of honoring, worshipping, and serving the Creator men choose to honor, worship, and serve creation. In other words, mankind makes the wrong response and turns their back on the truth—the light they have been given—and so instead of receiving more light—more truth—they receive less. A downward spiral starts—for Jew and Gentile alike—a downward spiral that results in more and more separation from God. This is what mankind has to be saved from. We are caught in a "sin whirlpool." We are being sucked inexorably down unless we call out to God for rescue.

I am fully confident that if a man or woman, no matter who, and no matter at what time in history they lived—if they will respond correctly to the light that they have been given, then God will respond and give them more light. God will save them from sin "by grace through faith … without works." Salvation is a gift from God that we cannot earn. We must only be willing to receive it. Most do not want the gift. Only a small remnant of mankind is willing to reach out and accept the gift from God’s loving hand.

Today we have additional revelation about God. We call it "Special or Specific revelation" in contrast to General Revelation. Special Revelation is the written Word of God—the Bible. The Bible gives mankind even more light. This is a two edged sword. On the one hand, more light makes those who receive it more responsible than ever to obey it. On the other hand, they have a greater chance to be "saved" because of the brighter illumination.

In summary: I would say that Biblical theology is inclusive. Every man of every age has the opportunity to be saved:

Ephesians 2:8-9--For by grace you have been saved through faith; and that not of yourselves, it is the gift of God; not as a result of works, that no one should boast.

An individual simply has to want the gift and receive it. The key word is gift. Pure character and pure thinking have nothing to do with it. Pure character and pure thinking come after salvation has occurred, after the relationship with God is restored. They are the result of salvation, not the basis of it. We are all impure and we cannot rid ourselves of sin. We have to receive the gift of God—eternal life. It is a gift, we do not earn it. We cannot earn it. Today, we simply receive it personally trusting God that the work of Jesus is sufficient.