You need to define monotheism and polytheism in such a way as to avoid conflating belief with worship. In other words, belief in the existence of gods is not the same as worshipping them. The statement "I am the Lord thy God ... and thou shalt have no other gods before me" implies (1) several gods EXIST but (2) the Jews were only allowed to WORSHIP one of them. It was only gradually that the other gods became demoted to daemons (literally: divine spirits) and even later that daemons turned into "demons" (evil divine beings). Kinneavy's book on Greek Rhetorical Origins of Christian Faith has a good discussion of this issue.
There is a lot of debate on this question and some of it is based on erroneous theories that have been debunked by archaeological evidence. One current idea is that, while past theories have held that since there are more than one name for God polytheism is indicated, comparative ancient history shows that it was quite common for one thing, place, entity to have more than one name. This supports ancient monotheism in ancient Hebrew religion.
Arguably, the prohibition against idolatry--a prohibition which would preclude polytheism--came about even earlier than Abraham, after the Flood. According to many sources, including commentary in the Talmud, God came to Noah after the Flood and gave him Seven Laws to follow to ensure morality. These laws include an admonition against the worship of idols -- considering that Noah spoke to God (either in dreams or through an intermediary), he would certainly understand the difference between a statue and the real thing.
I think you might look at this as Judaism was monotheistic from the beginning but surrounding cultures were not, so there was an interaction and possibly a clash between with Hebrews and other cultures. They might have been suspicious of them. It could explain a lot of the lingering resentment.
I think "the" event that turned the Hebrews into monotheists was Abraham's encounter with God and God's messengers. Abraham and his wife, Sarah, were very old, both in their nineties, but God promised that they would have a son. Of course, they were skeptical; what woman in her nineties could get pregnant? Yet that is exactly what happened: Sarah got pregnant and gave birth to a son, whom they named Isaac, which means "laughter," because she had laughed when told she would have a baby.
When God made the promise that they would have a son who would be the founder of a great nation, Abraham gathered all his male servants, and they all were circumcised as a sign that they believed in and would now follow God. From that day, Abraham and everyone associated with him worshiped the one God.
I agree that we need to turn to the Old Testament, and in particular, the Pentateuch (the first five books of the Old Testament) in order to help us answer this question. There we can see the blueprint that very clearly helped to define the Jewish faith and identify themselves as being distinct compared to the other groups and tribes that there were at the same time. In particular, you might like to consider how the Jewish creation myth diverges sharply in some key areas from other creation myths of the same time period.
Because the recording of the scriptures happened long after the events, we can look to that written record to find the actual occurrences. Probably the most forceful early statement of the instruction that the Hebrew people were to worship only the one God came as Moses was on Mt. Sinai receiving the Ten Commandments.