in the 6th entury BC the israelite king jehoiaikim refused to pay tribute (ie 'protection money') to the powerful Babylonians which resuted in the Baylonians attacking and defeating the Israelites. Consequently the israelite elite and part of the general poultion were removed from israel to babylon.
The exiled priests were concerned to preserve the ethic identity of the israelites and did so by creating an official mythology, in writing so it was immune from change, dilution or contamination from foreign ideas. It was a scheme that blurred nationalism and relligion, myth and history.
70 years later the babylonians were themselves defeated by the Persians under Cyrus. Cyrus permitted the exiled jews to return to jerusalem, making israel a vassal state of his empire. jewish royalty and aristocracy had been destroyed; the reconstitued Israel was highly theocratic.
For the next few hundred years israel changed hands repeatedly. However it remained a small minor theocracy on the fringes of world event.
By the time of Jesus, israel had passed from Greek control to the Romans, but most Isealites were poor, highly taxed subjects of foreign power. Traditional judaism was represented by a corrupt and venal priesthood and the mass of ordinary people were open to a very different vision.
Christianity has little in common with judaism. Judaism is ethnocentric and is not concerned with aterlife; Christianity is universal and salvation is central.
Christianity was more successful outside israel than with the Jews inside. However this is a period where there were any number of competing creeds and religions around the mediterranean. The dominance of Christianity was due to a historical accident - it was championed by a roman general who went on to become emperor. Almost at a stroke christianity was transformed from 'just another cult' to the official religion of the world's greatest empire.
islam is closely modelled on Judaism. In my view, islam was invented as a political device - it was intended to forge unity aross a pan-arabian empire containing a wide variety of ethnicities and religions.