It sounds like you actually know nothing about any of these religions!
Judaism obviously claims its story is continuous from the beginning of creation, but the timeline in its own narrative suggests approximately 7000 BC. At first this was oral tradition, but estimates as for when it was written down range from 900 BC to about 450BC.
As far as Christians are concerned, the last Jewish books chronologically were Ezra and Nehemiah, written approximately 400 BC. After the period recorded in this book, the Jews were waiting for their Messiah to arrive.
Christianity per se didn't start until after Jesus' death around (around 32 AD), and the first books were written between about 40AD and 70AD. But obviously, Christianity didn't even start until many centuries after the Jewish tradition was recorded in written form, because it needed Jesus to have been born first.
The selection of which books make up the bible today was decided upon by the Council of Nicea in the late 4th century AD, and is mostly unchanged to this day, although some religious groups also include some other books, collectively called the Apochrypha, in their bibles. Some argue these aren't important, others argue they are, but whatever in the 4th century, the leaders of the church from all around the world met up several times to choose to selection of books they felt were most important for people to know. It was mostly limited because paper was expensive then, and they wanted the minimal set that contained everything considered essential to Christianity.
The Jews continued writing and considered some books important after that point, but essentially 400 BC was the last significant event even in their canon.
Islam is much later than this, and certainly much later than Christianity. As I said above, the bible in its current form was decided on in the 4th century AD and the prophet Muhammad wasn't born until the 6th century AD. Most people date Islam to 610, which is when Muhammad recorded his first revelation. You can even see Islamic teaching that references Christianity - initially positive, recognising Jesus as a prophet from God, and later more combative when Islam was largely ignored by Christians as being unnecessary.
I've read more cynical interpretations that Muhammad was hoping to ally with Christians to avoid persecution, and when they all largely ignored everything he was saying, then he decided they too were infidels who oppose the will of God, and later parts of the Quran are distinctly anti-Christian in contrast to the earlier parts.
Muhammad also re-framed old Jewish stories (accepted as true by both Jews and Christians) in a way that tried to discredit their traditions, but paint Islam more favourably. The most contentious of these is regarding Abraham and Isaac - in the Jewish tradition, he and his wife Sarah had been childless for many decades after God had promised him that his children would have many children and become many nations. Finally had a son, and God asked him to sacrifice his firstborn as a test of his faith in God to provide another son. When God saw that he would be willing to obey him and perform the sacrifice, God tells him to stop, reaffirmed his promise to bless all nations through his son, and provided a substitute animal for the sacrifice. This is all in Genesis 22. The Islamic tradition, on the other hand, re-frames this as Abraham going crazy for some reason, trying to kill his only son after decades of being childless, and God having to stop in to stop him from murdering the son he'd been longing for for decades.
So, far from divergent history long before any written Jewish history, it's the complete opposite - Jewish history largely ends in 400 BC still waiting its Messiah; Christianity claims to be about that Messiah and covers the period from about 3 BC to around 40 AD, and was largely finished being recorded around 70 AD; Islam claims to have yet more revelation recorded between around 610 AD and 650 AD. If it wasn't for the fact that the previous believers didn't agree with the new revelations each time, you could consider them to be linear and not divergent at all, rather continuing from where the previous tradition finished.