Question: What happens to people who were born and died prior to the birth of Christ?
Response: This is a good question and one which is asked much more often than you would think. A corollary question also frequently asked is "what about people who die without hearing about Jesus" even after the cross. I like to say on these occasions that – whatever the answer to these questions – those who ask them have, in fact, heard about Jesus. The first point here being that even if there were mitigation for lack of faith in Christ on the basis of ignorance of the issue, that mitigation certainly would not apply to those who have heard the gospel. Paul makes this same point in Romans chapter ten regarding Israel in reply to the hypothetical statement that Israel didn't know that salvation came through faith rather than law (paraphrasing Psalm 19), demonstrating that, from the divine point of view, the construction of the universe itself is a witness to the world of God's existence and true nature (and therefore points the way to Him):
God's wrath is about to be revealed from heaven upon all ungodliness and unrighteousness – on men who suppress the truth [about God] in their unrighteousness. For that which can be known about God [from everyday experience] is obvious to them, because God has made it obvious. His nature, though invisible, is nevertheless plainly apparent, and has been since His foundation of the world, for it may be clearly inferred from this creation of His – [this is true of] both His eternal power and His divinity – so that they are without any excuse: they knew about God, but they neither honored Him as God nor thanked Him. Instead, they gave themselves over to [the] vanity [of this world] in their speculations, and their senseless hearts were filled with darkness. Claiming to be wise, they became foolish, for they exchanged the glory of the incorruptible God for images and likenesses of corruptible men, of birds and beasts and reptiles (i.e., idolatry).
This is an important point because it makes clear what the issue really is in the question you ask: God has always left Himself with a witness in the world (Acts 14:17), and indeed even the dividing up of the world's nations has been done for the express purpose of leading people to Him (Acts 17:26-28; cf. the Law of Moses which is a "pedagogue" for leading people to Christ for salvation through faith: Gal.3:24). But where there is no interest, God is not responsible for providing the specifics of the gospel. The whole Old Testament (spiritual) economy looked forward to the cross. In those times it was largely through the practice of animal sacrifice that gentiles and, following Abraham, Jews alike honored the promise of a coming Substitute who would atone for all sin (evidenced from the coats of skin worn by Adam and Eve and from Abel's sacrifices onward: Gen.3:21; 4:4-5; Heb.11:4; cf. Rom.3). The Father was just to patiently and mercifully set aside all sin committed before the cross because of that sacrifice which Jesus was foreordained to make on behalf of us all (1Tim.2:5-6; Heb.2:9; 1Jn.2:2; cf., Matt.20:28; Jn.1:29; 12:47; 3:16-17; 2Cor.5:19; 1Tim.4:10; 1Jn.3:5):
. . . Jesus Christ, whom God foreordained as a means of atonement [appropriated] through faith [and validated] by means of His blood (i.e., His sacrifice on the cross) to demonstrate His righteousness in overlooking the previously committed sins [of the world].
After the cross, we see that promise of a Savior to pay the price for us fulfilled in the flesh. Both before and after the cross, whether looking forward to it through shadows, or back on it through the clear light of day, we appropriate that sacrifice on our behalf through faith – through faith we make it plain to God, to the world, and to ourselves that we are not depending upon our own works or any other earthly solution to resolve the ultimate problem of death and judgment for sin, but are relying instead upon God and His solution, trusting in Him, believing in His Substitute, and choosing for Him through the grace He has made available in Jesus Christ.
For all those who are not interested in God, or are ignoring the problem of mortality and the need for the forgiveness of sin, there is not much point in providing detailed information about how it is that God has provided eternal life by judging Jesus in our place that we might live with Him forever (i.e., the gospel of eternal life through choosing for Jesus Christ). That is to say, for those who don't really want to live with God, why should God be concerned that they know how, especially given the fact that the entire world in which we live our short lives breathes and sings His existence at the same time that it reveals our sinfulness and reminds us of our impending departure from it. That would be a case of casting pearls before swine.
God's sacrifice of His only Son was no small thing, and He did it out of love so that everyone might be saved (Jn.3:16). Having paid a price we cannot even imagine (although Abraham's near sacrifice of Isaac is a deliberate allegory that we may appreciate to some degree what an awesome sacrifice this was for our Father to make: Gen.22; Heb.11:17-19; Jas.2:21-23), it is not surprising that scripture clearly states God's desire for every human being to be saved (1Tim.2:4; 2Pet.3:9; cf. Ezek.18:23; Matt.18:14; Jn.12:47; 2Tim.2:24-26). But God wants willing worshipers (Jn.4:21-25). He does not coerce the free will of any person to force them to choose for Him, to force them to believe in Jesus. Indeed, the entire point to our being here on earth, and the entire point to our continued residence here after we do believe in Jesus Christ, is to demonstrate beyond doubt to men and angels, to God and to ourselves, that this choice of ours for Jesus Christ, this desire to belong to God and to forsake the world, this choice is true, and genuine, and solid, and real.
An important part of understanding God's complete fairness and wisdom in working things in this way is understanding first His character. For instance, God is fair and just in His nature – He embodies justice and it is impossible for Him to be unjust. But even this element of His character is only derivative of the perfection that is Him. For His existence is completely independent of the known universe. Vast as it is, if God could be described in spatial terms, He would exceed the universe to an infinite degree. And God is independent of time. Like the universe, time is His creation and, like the universe, it does not constrain Him in anyway. God is all-wise and omniscient. He knows at once all that has ever happened in time and space, and all that ever will, and all that ever could happen, and since He is absolutely sovereign over time and space, nothing that has or will happen could or can do so without His will and without His prior decree. Much more could said here (see Bible Basics: Essential Doctrines of the Bible in Outline; Part 1: Theology: The Study of God for more), but this is a short way of saying that God knows very well who has chosen and is choosing and will choose for Him, and, conversely, all who have and are and will reject Him and the gift of His Son. God has unlimited power so that there is not only nothing He could not have anticipated within His creation and the history He has decreed (down to the number of hairs on our heads at any given time, as the scripture says), but there is also nothing that He cannot do whenever He wills to do it. With perfect knowledge, with absolute power, with perfect fairness, and with a desire for all His creatures to be saved so strong that He was willing to give up His only Son to death to save them, it stands to reason that God is not going to deny a single human being who wants to be saved the precious knowledge of His Son. The fact that by far the vast majority of people in the history of the world (and sadly also many of those belonging to putative Christian organizations in my reading of things) have chosen to reject Him and His Son in their hearts does not reflect any injustice or impotence or poor planning or hypocrisy or fickleness on His part. Rather it reflects the greatest glory upon Him – He did the most to save the few when He knew that the many would never respond to His gracious offer, no matter what He did, no matter what they knew. That is a picture of mercy, goodness, and grace that boggles the mind and should make any person with even an ounce of humility shout for joy and sing His praises.
Here as some other files posted to Ichthys that you might find helpful:
What about those who have never heard the gospel?
Peter's Epistles #11: "Natural and Special Revelation"
The Saving Work of Jesus Christ (in BB 4A: Christology)
Bible Basics 4B: Soteriology: the Study of Salvation.
Hope this is helpful to you,
Yours in Him who is the only way, the only truth, and the only life, our Lord and Savior Jesus Christ.