James Hoffmeier is a specialist in ancient Egypt who has written two books devoted to ancient Israel and their intersection with Egypt: Israel in Egypt: The Evidence for the Authenticity of the Exodus Tradition (1999) and Ancient Israel in Sinai: The Evidence for the Authenticity of the Wilderness Tradition (2005). In a recent essay he summarizes some of the reasons why there is not more archaeological evidence for Israel in ancient Egypt.
"First, the delta of Egypt, within which was the land of Goshen, where the Hebrews resided, is the least evacuated area of Egypt. Second, because of the moist environment of northern Egypt from millennia of annual Nile inundations, objects made from perishable materials do not survive. In fact, not a scrap of a papyrus document has survived from the delta from pharaonic times. Only a few Roman-era papyri have been found at Tanis, thanks to the carbonized condition of some that were kept in clay jars (a la the Dead Sea Scrolls). Third, those who excavate at delta sites are normally limited in accessing lower levels from earlier history, owing to high water tables. Archaeologists who employ a costly pumping system, such as at Tell el-Dab'a and Buto have been able to reach earlier strata. I have seen this system at work at Dab'a during an April 2002 visit. The scriptorium of the fifteenth-century palace was being excavated. Only clay bullae with seal impressions that once sealed papyrus documents were found, but not papyrus survived! The same was true in my own excavations at Tell el-Borg, where we discovered several mud bullae, and even though it is a desert setting, because of rain this area experiences, no papyrus was extant. Thus, when a biblical scholar points out that there is no Egyptian evidence to support the presence of the Hebrews in Egypt, or for the exodus, it is rash to conclude that this absence of evidence is evidence of absence."Hoffmeier goes on to add the following:
"The reality is that historians of the ancient Near East have often accepted the witness of written documents without corroborating archaeological data. During the fall of 2010, I participated in a conference in Germany on the exodus and conquest. In a panel discussion, a distinguished German colleague repeated the mantra that there is no Egyptian evidence for the exodus, which raises questions about the historicity of the biblical tradition. I asked if he believed that Thutmose III invaded Canaan in the mid-fifteenth century BC, besieging and taking the city of Megiddo. He responded, 'Of course.' Then I pointed out that this military campaign is one of the best documented reports from the ancient Near East as it is recorded both in royal sources (e.g., Annals of Thutmose III, Gebel Barkal Stela, Armant Stela, Buhen Temple Text, Karnak Seventh Pylon Text, Karnak Toponym lists) and in private documents and biographies of officers who accompanied the king. Despite all this textual evidence (from a variety of genres of literature) for the battle of Megiddo in 1457 BC and a seven-month siege of the city (according to the Barkal Stela), I reminded him, there is still no archaeological evidence from Megiddo for the Egyptian attack! Megiddo, as it turns out, is probably the most excavated site in ancient Israel, having been investigated with regularity since 1903, and work in ongoing. This scholar was prepared to accept the claims of various Egyptian texts, although they were shaped by religious, ideological, and propagandistic agendas, despite the absence of any clear archaeological evidence to support the written claims. I concluded my observation by saying that as historians were willing to give Thutmose III's written claims the benefit of the doubt, I was prepared to do the same for the exodus narratives." "'These Things Happened': Why a Historical Exodus is Essential for Theology" in Do Historical Matters Matter to Faith? A Critical Appraisal of Modern and Postmodern Approaches to Scripture edited by James K. Hoffmeier and Dennis R. Magary (Wheaton, Ill.: Crossway, 2012), 108-110.