There were slaves in Egypt, and sometimes whole groups of people were taken. Also at that period of time, there was also lots of movement of people from one area to another.
The big question is why would a group of people have as their origin story that they came from a distant land and were just a bunch of escaped slaves? Most origins of nations stories show that you were created there in the land you now inhabit, and therefore, have full rights and privileges. This is your land because you always had it.
There may be some truth to the exodus stories. Whether all people who later identified themselves as “Hebrews” were involved or that there were ten plagues can be called into question. But, something happened that created this very strange story of enslavement and rescue which was incorporated into the cultural teachings of that time.
Egypt, of course, doesn’t mention that it was visited by ten plagues and all their slaves escaped. They also don’t bother mentioning battles that they lost. Writing was for only the very upper strata of society, and what was written was the official history. If it made the king look good, it was written. If not, they didn’t bother mentioning it.
You don’t get a lot of unofficial written accounts until the times of the Greeks and Romans when writing was much more widespread and not controlled by a central authority.
A good percentage of the population of the Roman empire was Jewish. The Romans were getting tired of their old myths and were looking around for something more sophisticated. Zoroastrianism was big and so was Judaism. The Talmud mentions that there was quite a bit of outreach at that time. It was about the time of the Roman empire that the laws of conversion were established back then and so was the rule of matrilineal decent. This wasn’t an issue earlier when Jews were simply a self contained community. However, with the interest in the general Roman population, these new guidelines had to be clearly established. Before, being Jewish was mainly about simply following the law. There was no idea of official conversion.
The main problem with mass Jewish conversion is the amount of information and training you need. Imagine if someone goes to a city and says “Okay, everyone! You’re all Jewish.” Before these people could even begin practicing as Jews, they would have to learn about the laws of keeping kosher and the Sabbath. They would have to clean their houses, get new dishes. Throw out their food. People would have to be trained to be ritual slaughterers, teachers, and mohels.
One theory states that there was a massive Jewish conversion in the Roman empire, but it grew too fast for it to be under the control of the Rabbis. Many of these newly converted Jews simply didn’t have the knowledge of the commandments and rituals involved, and may not have cared all that much. This group later became the basis of Christianity’s rapid grown in the heart of the Roman empire. Paul’s teaching that you could find a way to God without having to do all those messy commandments probably found a strong voice in this community.