Over the past few years, attending various Seders on Passover, I have heard some secular people say that there is no archaeological evidence of Jews in Egypt during the bronze age when the story of the Exodus occurred. Similarly, no archaeological evidence of Jews in the wilderness for 40 years. As I will be conducting the Seder this year for many friends and family, I'd like to have an answer for this when the question comes up. It is vitally important to have an answer, as our entire religion is based on the Exodus story and receiving the Torah.
Firstly, it is worth noting that lack of evidence is not evidence of lack. IMSMC, modern archaeology has at least one case of an entire civilization that is know about only because of the accidental discovery of a lone artifact.
Secondly, it is important to acknowledge that profound biases are inherent to human research endeavors, particularly when researchers are devout ideologues. This is very often the case in academia, at least in the soft sciences such as archaeology. These biases color how evidence is interpreted. Along these lines, it is definitely worth reviewing some of the evidence presented by non-mainstream researchers, such as that presented here: https://www.amazon.com/Patterns-Evidence-Kevin-Sorbo-narrator/dp/B00Z9HS7TU and here: http://patternsofevidence.com/