All religions have some sort of founding myth that I can imagine people being skeptical towards, but the story of exodus seems to stand out as particularly unbelievable to the people who must have first heard it. The myth of jesus resurrection is far fetched, but it was only ever claimed that a small group witnessed it. How exactly did a myth like exodus gain traction if it claimed that many many thousands of people witnessed an event that never happened? Weren't people suspicious at the lack of witnesses when supposedly thousands existed?
The easy answer is that people believe their founding myths. We just do. Now for some other answers.
There are some textual clues that suggest the number of participants in the exodus may have been lower - for example there are 2 midwives for some six hundred thousand people, or is it six hundred families? - significantly decreasing the amount of people would make the story far more plausible, and in particular would make it easy to believe that they left no archaeological record.
A story like this, one that is powerful, gives a lot of meaning, has the potential to be picked up by people who were not directly involved, or adopted through marriage and so on. There is no debate over whether or not Jews existed at this time, or at least the people who went on to become the Jewish nations, and the shared history of being under Egyptian rule (the region was ruled by Egypt several times) made this sort of a story relevant even to those who thought that their families weren't a part of this origin story. And in a very few generations following ANY such story, people in the region would all be related enough to claim it as their own anyways.
Early archaeological evidence of the precursors to the Hebrews suggests they were nomadic people who settled in the highlands, yet another reason why people would feel that "this is my story" and buy in to it.
In summary - this myth was likely the story of a smaller community than described, and probably reflected some events that did happen to them (on whatever scale - at some scale it's impossible to argue for or against the historicity of a lot of events). Large portions of it were absolutely true for those who adopted it - tension with Egypt, tensions with giving up a nomadic life for a largely settled one, tensions over land, and so on, and the narrative was a really well-built way of giving shape to a lot of the questions people faced, and the conflicts that existed in their lives. People had no reason to question it.