One of the reasons the theologians of the past came up with the idea that the 430-year reference to the children of Israel dwelling in the land of Egypt started with Abraham was a result of their misreading this verse:
Galatians 3:16 Now to Abraham and his seed were the promises made. He saith not, And to seeds, as of many; but as of one, And to thy seed, which is Christ.
17 And this I say, that the covenant, that was confirmed before of God in Christ, the law, which was four hundred and thirty years after, cannot disannul, that it should make the promise of none effect.
Abraham is first mentioned, and it speaks of the covenant, and then makes reference to the 430 year period, at the end of which the law was given. Misreading this, and not seeking to harmonize all the Bible has to say about the subject, the theologians of the past mistakenly think that the 430 years begins with Abraham.
Of course, given that Exodus 12:40,41 tells us that the dwelling of the children of Israel was 430 years in Egypt, there's no way that the 430 years could have begun with Abraham. Abraham was never part of "the children of Israel"; in fact, the Bible speaks of him often as being the father of the children of Israel.
What the theologians missed in Galatians 3:16,17 is the word "confirmed". The covenant was confirmed—and following this confirmation was a span of 430 years at the end of which the law was given.
But who did God confirm the covenant with?
Anyone who reads the Bible comes across constant references to Abraham, Isaac, and Jacob. The Lord first gave the promise of the land of Canaan as an everlasting possession to Abraham. But He reiterated this promise to Isaac and to Jacob. Abraham lived 100 years in the land of Canaan and then died. Isaac lived for 180 years in the land of Canaan and then died. Jacob, however, lived for 130 years in the land of Canaan before experiencing a very traumatic event—a terrible famine forced him to come out of the promised land of Canaan and to enter into Egypt to come under the protection of his son Joseph. Before going down into Egypt, God visited with Jacob (Israel) and said to him:
Genesis 46:2 And God spake unto Israel in the visions of the night, and said, Jacob, Jacob. And he said, Here am I.
3 And he said, I am God, the God of thy father: fear not to go down into Egypt; for I will there make of thee a great nation:
4 I will go down with thee into Egypt; and I will also surely bring thee up again: and Joseph shall put his hand upon thine eyes.
Certainly, these words greatly comforted Jacob as he left the land promised to Abraham, and to his father Isaac, and to himself, for the land of Egypt. God confirmed the covenant with him by telling him, "I will also surely bring thee up again.” That is, the Lord was assuring Jacob that He would not forget the promise given to the patriarchs concerning Canaan as an everlasting habitation.
How do we know God confirmed the covenant with Jacob? We know because God tells us that He did:
Psalm 105:8 He hath remembered his covenant for ever, the word which he commanded to a thousand generations.
9 Which covenant he made with Abraham, and his oath unto Isaac;
10 And confirmed the same unto Jacob for a law, and to Israel for an everlasting covenant:
Once we understand that Galatians 3:16,17 is telling us about God's confirming the covenant with Jacob at the point he was going to enter into Egypt, then we once again have perfect harmony with all Scripture. Jacob entered into Egypt in 1877 BC, and 430 years later, the children of Israel came out on the selfsame day in the year 1447 BC (1877 - 1447 = 430 years). And once we find this type of agreement, we know we have learned the truth of what the Bible is teaching.