About two years into the great worldwide famine, at Joseph’s request, his father Jacob’s family came to Egypt to live there.
[Joseph said] “7 “God sent me [here to Egypt] before you to preserve for you a remnant in the earth, and to keep you alive by a great deliverance.” (Gen 45:7 NAS95)
It would appear that this promise was already being fulfilled during the 17 years that Jacob lived in Egypt prior to his death, or at least Jacob began to see an encouraging fruitfulness among his own children, grand-children, and great grand-children. Considering that Jacob is Abraham’s grandson, this is roughly 200 years after the promise was given to Abraham. God promises to preserve and deliver His people in a mighty way.
“27 ¶ Now Israel lived in the land of Egypt, in Goshen, and they acquired property in it and were fruitful and became very numerous. 28 Jacob lived in the land of Egypt seventeen years; so the length of Jacob’s life was one hundred and forty-seven years.” (Ge 47:27-28 NAS95)
After Joseph died, the young people group now known by Jacob’s new name Israel (Gen 32:28), continued to multiply, which caused Pharaoh grave concern.
“6 Joseph died, and all his brothers and all that generation. 7 but the sons of Israel were fruitful and increased greatly, and multiplied, and became exceedingly mighty, so that the land was filled with them.” (Ex 1:6-7 NAS95)
“[Pharaoh] said to his people, “behold, the people of the sons of Israel are more and mightier than we.” (Ex 1:9 NAS95)
So, we see that Israel’s faithfulness to the promise of God regarding fruitfulness is leading to an explosion in the population of nascent Israel. This is the Abrahamic promise of “nation”.