The apostles and the early Christians were Jewish monotheists, believers in a faith that accepted one undivided God, but in Jesus they encountered a new religious situation that forced them to re-appraise their understanding of God. In meeting and walking with Jesus Christ they had a sense that they were in a special presence, one of extreme charisma and authority, a person who exhibited spiritual impact and whose words could speak to the depths of the human heart and mind. Furthermore, Jesus' claims made before Caiaphas, which would have been blasphemy from a mere human, had been approved by God, who at the resurrection reversed the death sentence passed on him. So problems solved? No the next lot of problems were just beginning.
The ancient world had no difficulties with the concept of sons of God, divine beings in human form; and it had no difficulties with gods adopting human form, generally to seduce girls, who would then breed heroes. But this claim of an incarnation came within a religion, Judaism, which had set its mind against all such possibilities. There was also the scandal of the cross to deal with. The humiliating death of Christ was not what you would expect from a son of God. The resurrection changed the situation, but even afterwards the risen Lord did not wreak revenge on his enemies, as a divine being might, but greeted his apostles with "Peace be with you." which was the equivalent of hi. So during the first century the church had not only to make sense of Jesus' nature, but had to ask the question, why was God incarnate in Jesus and why in this particular life?
The gospels tell us that Jesus prophesied his own passion, saying that the Son of Man had to give his life as a ransom for many.Scholars disagree as to whether he said this or whether later views were being projected backwards into the gospel, which put words into Jesus' mouth. However, Jesus was bright enough to see where his life was heading, especially as his clash with the authorities was mounting, so I disagree with the view that the texts are words put into Jesus' mouth.
Paul set us on the path early. Years of quiet reflection before he began his mission led him to see that the key to understanding was the cross, which rather than being an embarrassing scandal was integral to God's scheme of salvation. Throughout his letters he speaks of the saving death of Jesus on the cross. Jesus was the lutron, which was a term that denoted the ransom paid to free a slave. In his use of this term he seems to have been taking Jesus' use and reflecting on it. The human race had fallen into slavery to sin and all deserved punishment, but in Jesus God himself had paid the price and so human were now free.
The letter to the Hebrews, probably not written by Paul, but by his friend Apollos, a scholarly Jew, presents the issue in different, but compatible terms. Jesus was the perfect high priest who offers himself as victim. The high priest in the temple had to sacrifice for his own sins, but then Christ, as the sinless one, could offer the perfect sacrifice and so his sins paid for all the sins of humanity. We often hear it said that Christ's death opened the gates of heaven, which were shut till then, but this is a caricature. Writing in Jesus of Nazareth Benedict the Sixteenth makes the point that the gates of heaven are metaphorically in the risen Christ, and so heaven exists only where the risen Christ is. Before the resurrection heaven as we know it did not exist. This does not mean that there was no afterlife, but it was not heaven.