Why did Israel become a nation while in Egypt?
Israel became a nation in Egypt because God sovereignly placed them there after Joseph was sold, allowing them to multiply and prosper in Goshen. Though they went down due to sin, this was part of God's redemptive plan to form and later redeem His covenant people.
Les explains that when the brethren sold Joseph into Egypt and all twelve sons ended up there because of sin, God lost control of His covenant people and had to set up a plan of redemption to buy them back. This was all in His sovereign plan. Israel ended up in Egypt, and while there they became a nation. Jacob went down into Egypt in the middle of the 430-year span God had foretold—215 years after Abraham's call, with 215 years left. As long as Joseph lived, things went well for the Israelites; they had it good in Goshen, the best productive area near the Nile, and as they prospered, they multiplied.