As God continued to sovereignly and mercifully call people to fellowship with him, sacrifices remained essential. God was holy, and man wasn't. So the death of an animal acted as a sort of "satisfaction" to God for man's sin. But this was only temporary at best, as God's wrath against sin could never be turned away by anything less than holy. So for centuries to come man continued to sacrifice every year in order to be right with God.
But these imperfect sacrifices were actually pointing to something greater that God was providing — the perfect sacrifice of himself. Frankly, that's exactly what God did when he sent Jesus into the world: He gave us himself as a sacrifice for our sins. Jesus, the holy God in the form of a man, lived a sinless life, died a sacrificial death, and rose again from the grave so that all who believe in him could forever be made right with God. When Jesus accomplished this, God was satisfied permanently. Why? Because the sacrifice was holy. Perfect. It was the sacrifice of himself.
This was startling and world-changing good news — God had come to man and had given his life for us so that we would not die in our sins. As people heard this message, and saw how glorious God was in his sacrifice for sin and authority over death, people repented of their sins, believed this message and worshiped God for saving them. They, too, were now enjoying forgiveness from sin and fellowship with God, just as many others before them.
Even now, God, just as he has been doing since the beginning of time, is still calling people to himself through this very same message of his sacrifice, what we know as the Gospel. It is the good news that Jesus has come, has lived and died, and has risen as the complete atonement and satisfaction for our sins. And anyone who repents of his or her sin, turns to God in faith, and confesses Jesus as Lord and Savior, will be saved by God and made right with him forever. Incredibly, it is in this very act of saving lost sinners that God gets glory from us and has fellowship with us, the very thing he set out to do in the beginning.
Hallelujah for the story, and all glory to the Author!