Why does God hate babies who have not sinned?

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They did write about it. Letters from the Saul of Tarsus, the historical biographies of Jesus life, they have been found and preserved. These are primarily historical documents.

It wasn't until later that the church compiled these into a book that we now know as the Bible.

Jesus

The Christian gospels were written primarily as theological documents rather than historical chronicles.

Separate non-Christian sources used to establish the historical existence of Jesus include the works of 1st century Roman historians Josephus and Tacitus.

So, we know that the Romans didn't hide Jesus's existence. But there are no Roman records of his miracles.

The historical existence of Jesus as a person is a separate issue from any religious discussions about his divinity, or the theological issues relating to his nature as man or God.

A number of relics associated with Jesus have been claimed and displayed throughout the history of Christianity. Some people believe in the authenticity of some relics; others doubt the authenticity of various items. For instance, the sixteenth century Catholic theologian Erasmus wrote sarcastically about the proliferation of relics, and the number of buildings that could have been constructed from the wood claimed to be from the cross used in the Crucifixion of Christ.[328] Similarly, while experts debate whether Christ was crucified with three or with four nails, at least thirty Holy Nails continue to be venerated as relics across Europe.

No documents written by Jesus exist, and no specific archaeological remnants are directly attributed to him.

Historical reliability of the Gospels

There is no archaeological evidence supporting the existence of a historical Jesus or any of the apostles, although various other details mentioned in the gospels have since been verified by archaeological evidence, such as the actual existence of the Roman Governor Pontius Pilate, the procurator who ordered Jesus' crucifixion, and the Pool of Bethesda.

Luke's reliability as a historian is questioned. Thomas Howe examined Luke's description of Paul's sea journeys, including Luke's references to thirty-two countries, fifty-four cities, and nine islands, and stated that he could not find any mistakes.[150] However Powell states that Luke’s knowledge of Palestinian geography seems so inadequate that one prominent scholar was led to remark “Jesus route cannot be reconstructed on a map, and in any case Luke did not possess one”.[149] Powell states that “if Luke intended to write history he did so poorly, but he did not so intend. Luke was a theologian, not a historian.[149][149] A narrative which includes supernatural phenomena such as angels and demons is problematic as a historical source."