"There ought to be a law against that!" says David.
"I'm sorry but there isn't one." replies Richard.
"Then let's make one!" exclaims David.
"Well, we could, I suppose," explains Richard, "but we wouldn't be able to catch this lot because laws don't operate retrospectively."
This is what Paul is explaining. The Law can have nothing to do with Abraham because Abraham lived hundreds of years before Moses was given the Law. God made a promise to Abraham even before he left Haran and it is through this promise we are saved. "All people on earth will be blessed through you." Genesis 12:3. This covenant promise was made by God in an unconditional way. It did not depend on the behavior of Abraham or any of his descendants.
Paul takes an example from everyday life (Galatians 3:15). The example is a last will or testament. Once it is signed, sealed and delivered after a person's death, it cannot be altered. So long as the testamentor was of sound mind and the will was properly witnessed, the cats' home is going to benefit and not the long-lost cousin in Australia. God made a covenant with Abraham and God will deliver.
But this passage in Galatians has two major problems. The first is how Paul goes on about singular and plural 'seeds'. In English this doesn't make much sense to us, since 'seed' is a collective noun; it can mean one seed or many. The same is true for both Hebrew or Greek, the languages that Paul might have been referring to.
The second is the 430 years since the promise was given. On some accounts this seems to be an underestimate; some interpreters put the period as 645 years. I don't want to go into a great deal of detail about this; it seems to me to fall into Paul's category of arguing about meaningless genealogies, but I suspect that the answer to both questions lies in the fact that the promises were repeated in Genesis 22:18 to Abraham, in 26:4 to Isaac and 28:14 to Jacob. And with each repetition there is a choice between plural seeds and singular seed. It was to Isaac not Ishmael that the promise was given, and to Jacob not Esau and as a matter of fact to Judah and not the 11 other sons. Not to Levi, through whom the priesthood and Mosaic law derived; not even through Benjamin, from whom we have the writer of most of the New Testament and the greatest preacher ever. It is through Judah, that seed, that we have the Christ, the fulfillment of all prophesy and promises.
If the inheritance depends on the law; it no longer depends on a promise. What sort of a promise is it that it takes the law to enforce it? God in his grace gave the inheritance to Abraham through a promise. Our salvation depends on a promise.
As a father, I have often fallen down on my promises. Life encroaches and one forgets. But this was a promise from God. The all-seeing, all-powerful God. He does not renege; he does not forget. Our salvation is all of grace; none of works. We bring nothing to the party except our sins - and these to be washed away.