Objection 1. It seems that there should have been no sacraments after sin, before Christ. For it has been stated that the Passion of Christ is applied to men through the sacraments: so that Christ's Passion is compared to the sacraments as cause to effect. But effect does not precede cause. Therefore there should have been no sacraments before Christ's coming.
Objection 2. Further, sacraments should be suitable to the state of the human race, as Augustine declares (Contra Faust. xix). But the state of the human race underwent no change after sin until it was repaired by Christ. Neither, therefore, should the sacraments have been changed, so that besides the sacraments of the natural law, others should be instituted in the law of Moses.
Objection 3. Further, the nearer a thing approaches to that which is perfect, the more like it should it be. Now the perfection of human salvation was accomplished by Christ; to Whom the sacraments of the Old Law were nearer than those that preceded the Law. Therefore they should have borne a greater likeness to the sacraments of Christ. And yet the contrary is the case, since it was foretold that the priesthood of Christ would be "according to the order of Melchisedech, and not... according to the order of Aaron" (Hebrews 7:11). Therefore sacraments were unsuitably instituted before Christ.
On the contrary, Augustine says (Contra Faust. xix) that "the first sacraments which the Law commanded to be solemnized and observed were announcements of Christ's future coming." But it was necessary for man's salvation that Christ's coming should be announced beforehand. Therefore it was necessary that some sacraments should be instituted before Christ.
I answer that, Sacraments are necessary for man's salvation, in so far as they are sensible signs of invisible things whereby man is made holy. Now after sin no man can be made holy save through Christ, "Whom God hath proposed to be a propitiation, through faith in His blood, to the showing of His justice... that He Himself may be just, and the justifier of him who is of the faith of Jesus Christ" (Romans 3:25-26). Therefore before Christ's coming there was need for some visible signs whereby man might testify to his faith in the future coming of a Saviour. And these signs are called sacraments. It is therefore clear that some sacraments were necessary before Christ's coming.
Reply to Objection 1. Christ's Passion is the final cause of the old sacraments: for they were instituted in order to foreshadow it. Now the final cause precedes not in time, but in the intention of the agent. Consequently, there is no reason against the existence of sacraments before Christ's Passion.
Reply to Objection 2. The state of the human race after sin and before Christ can be considered from two points of view. First, from that of faith: and thus it was always one and the same: since men were made righteous, through faith in the future coming of Christ. Secondly, according as sin was more or less intense, and knowledge concerning Christ more or less explicit. For as time went on sin gained a greater hold on man, so much so that it clouded man's reason, the consequence being that the precepts of the natural law were insufficient to make man live aright, and it became necessary to have a written code of fixed laws, and together with these certain sacraments of faith. For it was necessary, as time went on, that the knowledge of faith should be more and more unfolded, since, as Gregory says (Hom. vi in Ezech.): "With the advance of time there was an advance in the knowledge of Divine things." Consequently in the old Law there was also a need for certain fixed sacraments significative of man's faith in the future coming of Christ: which sacraments are compared to those that preceded the Law, as something determinate to that which is indeterminate: inasmuch as before the Law it was not laid down precisely of what sacraments men were to make use: whereas this was prescribed by the Law; and this was necessary both on account of the overclouding of the natural law, and for the clearer signification of faith.
Reply to Objection 3. The sacrament of Melchisedech which preceded the Law is more like the Sacrament of the New Law in its matter: in so far as "he offered bread and wine" (Genesis 14:18), just as bread and wine are offered in the sacrifice of the New Testament. Nevertheless the sacraments of the Mosaic Law are more like the thing signified by the sacrament, i.e. the Passion of Christ: as clearly appears in the Paschal Lamb and such like. The reason of this was lest, if the sacraments retained the same appearance, it might seem to be the continuation of one and the same sacrament, where there was no interruption of time.
Source: Summa Theologica (New Advent)