While I’m sure there are a number of historical and archeological arguments for the historicity of the Exodus, I found this passage Andy Crouch’s Culture Making compelling for its brevity and force:

The exodus does not just have religious significance. It stakes a claim to human history. To be sure, more than a few moderns question whether the events recounted in the Bible happened the way they were recorded. Undoubtedly the biblical texts, like all texts, streamline or condense certain features of the historical events. Yet those who would deny the basic historicity of the exodus, like those who would deny the historicity of the resurrection, are left with a daunting historical problem: how to convincingly explain the coming into being of such a distinctive people, with such deeply rooted and enduring religious, ethical, and cultural practices, without any cataclysmic event like the deliverance from Egypt. One need only compare the exodus account to the crazy quilt of national origin stories in Greek or Roman mythology. We have to admit a pantheon filled with a wild variety of gods of various sort and conditions, playing favorites, and capriciously intervening in history in an endless cosmic competition, seems much better suited to the haphazard process of cultural consolidation in the ferment of the Mediterranean Basin than the idea of a single Creator God who has chosen a particular people and sticks with them with the ferocity of covenant love. Even in spite of their admitted temptations to assimilation and syncretism, even through cycles of marginalization and exile, the Jewish people maintained a tenacious and culture-shaping faith in that one God, YHWH They did so despite living, generation after generation, in cultural contexts where monotheism in general and worship of YHWH in particular was all but impossible. In the face of such and extraordinary religious and cultural achievement, something like the exodus comes much closer to being the simplest and most plausible explanation.

–Culture Making: Recovering Our Creative Calling, pg. 204-205

In essence, “How do you explain the Jews without the Exodus?” You can’t.