A case for infant baptism

I was reading in Martin Luther's Commentary on Galatians (yes, I know, it seems like the only thing I've been reading lately) and what I read was really interesting. It never dawned on me until this afternoon that God bestowed upon Abraham the promises many many many years before God gave Moses the law. Here's the quote from Luther:

Galatians 3:17 says: "This is what I mean: the Law, which came four hundred and thirty years afterward, does not annul a covenant previously ratified by God, so as to make the promise void."

Here's what Luther says about this verse:
"God acted properly in giving the promise such a long time before the Law, lest it be said that righteousness is given through the Law, not through the promise. Moreover, it was intentional that He preceded the Law with the promises; for if He had wanted us to be justified by the Law, He would have given it four hundred and thirty years before the promise or certainly with the promise. But now He is completely silent about the Law at first; He establishes it finally after four hundred and thirty years. Meanwhile, for that entire time, He speaks about His promises. Therefore the blessing and the gift of righteousness came before the Law, through the promise. And therefore the promise is superior to the Law. Thus the Law does not abrogate the promise. But faith in the promise, by which believers were saved even before Christ was revealed, and which is now being preached through the Gospel to all the nations of the universe, destroys the Law, so that it can no longer increase sin or terrify sinners or reduce to despair those who take hold of the promise by faith.
"A great emphasis, or rather irony, is concealed in Paul’s explicit reference to four hundred and thirty years. It is as though he were saying: “If you understand arithmetic, count on your fingers what the interval is between the giving of the promise and the Law. Certainly there was a promise a long time ago, even while there was no Law (that is, for four hundred and thirty years).” Therefore this is a rather vigorous argument based on a specific interval.
"Here Paul is not speaking about the Law in general but only about the written Law. It is as though he were saying: “God could not regard our worship, works, and merits that did not yet exist, because there was as yet no Law that commanded worship, required works, and promised life to those who kept it. ‘He who does them’ He says ‘shall live by them.’ Thus if I were to give a field or a house to a man to whom I owed nothing and did so not out of constraint but purely out of good will, and if after twenty or more years had passed since I did him this favor I imposed a law upon him about doing this or that, he could not say that he had merited the favor by his works when he had received it from me so many years before by sheer grace, without my having requested anything of him. In the same way God could not regard works and merits that preceded righteousness, because the promise and the gift of the Holy Spirit came four hundred and thirty years before the Law.” This is what Paul stresses in irony."

Hopefully you can figure out what I'm thinking without my articulating it.