The first question one would have to answer is is the account of the Exodus accurate, historically.

There is much debate about this and scholars fall on varying sides from 'didn't happen at all' (Finkelstein and Silberman) to 'probably happened but was not the same in number' (Friedman and some others).

The most interesting book I have read on this recently is Friedman's Exodus^1 which argues for the arrival of 2 main groups inside the 'Holy Land' the second later group being the Levites who were in Egypt/From Egypt although whether they were slaves is still some debate. Which Friedman goes into, and notes examples of items like they had knowledge of Egyptian brickmaking techniques compared to Canaanite techniques. Moses is an Egyptian name, he gives some other examples however I don't have the text in front of me at the moment.

The early tribes in Israel would have come (or risen to power) and conquered/Mixed with the tribes already in Canaan and taken on some of their deities, some of the early types would have been El and Baal, for example, we note that some of the early creation stories map to Canaanite creation stories.

The earliest person we know of to accept the Israelite religion was Abraham as per the Torah itself, and there is evidence for someone like an Abraham around 1800 B.C.E. But there's no direct connection. What we can see is the common earliest reference to Israel as a unique entity which is in the Merneptah Stele, which dates to around 1200 BCE, although some scholars have identified a possible reference to Israel (the text is not complete, however) on a pillar in Egypt going back as far as 1400 BCE.^1.

So we know that the Israelites spread out and mixed with Canaanite cultures and were a part of them but eventually, the culture (and religion) of the Israelites eventually won out and developed into its own distinct religion. This would have been in the time of the Iron Age I (1200-1000 BCE). Going back to Friedman here, he shows genetic and historical evidence that the Levites come in and adapted themselves as another Tribe and planted the Exodus story among the existing (forming) Israelites. This Iron Age I would have been when this happened. This Yahewism would have been the basis for monotheism. This could have been from the Levites who brought the YHVH diety with them from the Midianites and supplanted it over the others.

However, there were pockets of idolatrous worship especially on the North for some time. Statuettes of different home or hearth goddesses have been found near Tel Dan for example in the Temple there. This Temple in Northern Israel would not have been condoned by the people in Judea and would have been in a contest with it (Schiffman^3) as the Priests in Judea (First Temple) would have felt the only true Temple was the one in Jerusalem. Really some forms of idolatry continued into the First Temple period and in the Second Temple period, it would have most likely been Monolatry (accepting that others deities could exist along theirs). The clearest case for this is the changes to the Shema (Duet 6:4) which at that time read: “Hear, O Israel! The Lord is our God, the Lord alone.” this statement defines the deity YHVH as the one for Israel although it allowed for other cultures to have theirs as well. This is shown in sources such as the Septuagint and in the Nash Papyrus in the Second Temple period. An amulet found in Halbturn, Austria called The Halbturn amulet shows the current version (in Greek) as we now know it to be “Hear, O Israel! The Lord is our God, the Lord is One.”

So to sum all that up, the historical evidence points to a polytheistic culture that developed into a monotheistic culture.

Because in between the Exodus and the Promised Land it wasn't strictly Judaism yet, was it?

Which type of Judaism? Current Judaism is Rabbinic Judaism which takes the written tradition (Torah) plus the Oral Tradition (Talmud/Mishna) this developed most notably in the Babylonian Exile, prior to that there was the Temple Cult.