If the Jews were enslaved for 400 years by the Egyptians, why has archaeology not found anything to support that?

Skeptics have pointed out that, for all the attention that the Exodus draws, in their view, there are no ancient Egyptian texts that mention the Hebrews, there seems no evidence of Egyptian impact on Hebrew architecture, and there’s no proof the Hebrews were ever in Sinai. This conclusion is actually incredibly wrong. We have archaeological findings in Egypt that tell us that their ancient empire conducted huge building projects, using slave labor in the process, including “Asiatics,” their designation of any peoples originating east of Egypt—including Hebrews. This corresponds with the narratives of the book of Exodus that tell us that the Egyptians enslaved the Hebrews and made them work for them; [T]hey put slave masters over them to oppress them with forced labor, and they built Pithom and Rameses as store cities for Pharaoh—Exodus 1:11. Archaeologists have found evidence in the Nile delta region of northern Egypt, the land formerly known as Goshen, of Hebrew-styled architecture of a kind found in Canaan, along with a substantial treasure trove of Hebrew artifacts. We know that the Hebrews settled in Goshen: Then Joseph said to his brothers and to his father’s household, “I will go up and speak to Pharaoh and will say to him, ‘My brothers and my father’s household, who were living in the land of Canaan, have come to me. The men are shepherds; they tend livestock, and they have brought along their flocks and herds and everything they own. When Pharaoh calls you in and asks, ‘What is your occupation?’ you should answer, ‘Your servants have tended livestock from our boyhood on, just as our fathers did.’ Then you will be allowed to settle in the region of Goshen, for all shepherds are detestable to the Egyptians”—Genesis 46:31-34. And that’s exactly what happened: Joseph went and told Pharaoh, “My father and brothers, with their flocks and herds and everything they own, have come from the land of Canaan and are now in Goshen.” He chose five of his brothers and presented them before Pharaoh. Pharaoh asked the brothers, “What is your occupation?” “Your servants are shepherds,” they replied to Pharaoh, “just as our fathers were.” They also said to him, “We have come to live here awhile, because the famine is severe in Canaan and your servants’ flocks have no pasture. So now, please let your servants settle in Goshen.” Pharaoh said to Joseph, “Your father and your brothers have come to you, and the land of Egypt is before you; settle your father and your brothers in the best part of the land. Let them live in Goshen. And if you know of any among them with special ability, put them in charge of my own livestock”—Genesis 47:1-6.
We also know that they became property owners: Now the Israelites settled in Egypt in the region of Goshen. They acquired property there and were fruitful and increased greatly in number—Genesis 47:27. Thus, finding uniquely Hebrew architecture would make complete sense in a time and place where they were property holders. Continuing on, evidence has been found in Egyptian records containing Hebrew names in the records of Egyptian households, suggesting household slaves. Why would Egyptian households have records of Hebrew names? Ancient Egypt also documented a people of “sheepherders” who did not worship the sun god Ra. And we have found textual evidence found at several Egyptian sites that talk of “the nomads of Yahweh,” suggesting that Egyptians knew the Hebrews relatively well, including their religious practices and economic lifestyle. From our understanding of Egyptian calendars and chronology, we have come to learn that the Exodus took place about 1446 BC and, further, that the land of Canaan began feeling the impact of newly arriving people in about 1400, which fits in well with the 40-year wandering of the Hebrews in the Sinai desert. A discovery called the “Amarna Letters” talks about a people called the “Habiru”—possibly a derivative of “Hebrew.” These letters also show the Habiru to be a people who became through a campaign of conquest the dominant people-group in Canaan. There has also been a discovery called the “Ipuwer Papyrus,” essentially an ancient Egyptian poem which seems to contain allusions to what we know as the 10 plagues.
Why is there resistance to the whole idea of an Exodus? Again, it is an opportunity to discredit Scripture that allows skeptics to then question other fundamental pieces of the Bible. Certainly a perceived lack of credible evidence would allow someone to question its historicity. And, for someone who supports the idea of a material, naturalistic world, one cannot accept an historical narrative that includes tales of miracles. Exodus is full of them.
There have also been practical rebuttals to those who say the Exodus never happened—most of which come from the perspective of the so-called “arguments from silence”: One is that nomadic peoples never leave anything of lasting archaeological scope behind. Another is that Egypt would have never recorded anything of an embarrassing nature—such as the loss of their slave population. Certainly we see examples of that in ancient history—the Assyrian king Sennacherib’s lack of textual evidence for the conquest of Jerusalem after extensive texts detailing his many conquests in Israel and Judah up to that point. Even today, the nation of Japan has often remained silent when discussing various aspects of its activities in World War II.
However, we can know that there is substantial historical and archaeological evidence to lead us to confidently conclude that the Hebrews did live in Egypt, were enslaved by them, and then left them, wandering in the wilderness for an extended period before boldly coming into the land of Canaan.