Objection 1. It seems that Baptism was instituted after Christ's Passion. For the cause precedes the effect. Now Christ's Passion operates in the sacraments of the New Law. Therefore Christ's Passion precedes the institution of the sacraments of the New Law: especially the sacrament of Baptism since the Apostle says (Romans 6:3): "All we, who are baptized in Christ Jesus, are baptized in His death," etc.
Objection 2. Further, the sacraments of the New Law derive their efficacy from the mandate of Christ. But Christ gave the disciples the mandate of Baptism after His Passion and Resurrection, when He said: "Going, teach ye all nations, baptizing them in the name of the Father," etc. (Matthew 28:19). Therefore it seems that Baptism was instituted after Christ's Passion.
Objection 3. Further, Baptism is a necessary sacrament, as stated above (, 4): wherefore, seemingly, it must have been binding on man as soon as it was instituted. But before Christ's Passion men were not bound to be baptized: for Circumcision was still in force, which was supplanted by Baptism. Therefore it seems that Baptism was not instituted before Christ's Passion.
On the contrary, Augustine says in a sermon on the Epiphany (Append. Serm., clxxxv): "As soon as Christ was plunged into the waters, the waters washed away the sins of all." But this was before Christ's Passion. Therefore Baptism was instituted before Christ's Passion.
I answer that, As stated above (Question 62, Article 1), sacraments derive from their institution the power of conferring grace. Wherefore it seems that a sacrament is then instituted, when it receives the power of producing its effect. Now Baptism received this power when Christ was baptized. Consequently Baptism was truly instituted then, if we consider it as a sacrament. But the obligation of receiving this sacrament was proclaimed to mankind after the Passion and Resurrection. First, because Christ's Passion put an end to the figurative sacraments, which were supplanted by Baptism and the other sacraments of the New Law. Secondly, because by Baptism man is "made conformable" to Christ's Passion and Resurrection, in so far as he dies to sin and begins to live anew unto righteousness. Consequently it behooved Christ to suffer and to rise again, before proclaiming to man his obligation of conforming himself to Christ's Death and Resurrection.
Reply to Objection 1. Even before Christ's Passion, Baptism, inasmuch as it foreshadowed it, derived its efficacy therefrom; but not in the same way as the sacraments of the Old Law. For these were mere figures: whereas Baptism derived the power of justifying from Christ Himself, to Whose power the Passion itself owed its saving virtue.
Reply to Objection 2. It was not meet that men should be restricted to a number of figures by Christ, Who came to fulfil and replace the figure by His reality. Therefore before His Passion He did not make Baptism obligatory as soon as it was instituted; but wished men to become accustomed to its use; especially in regard to the Jews, to whom all things were figurative, as Augustine says (Contra Faust. iv). But after His Passion and Resurrection He made Baptism obligatory, not only on the Jews, but also on the Gentiles, when He gave the commandment: "Going, teach ye all nations."
Reply to Objection 3. Sacraments are not obligatory except when we are commanded to receive them. And this was not before the Passion, as stated above. For our Lord's words to Nicodemus (John 3:5), "Unless a man be born again of water and the Holy Ghost, he cannot enter into the kingdom of God, seem to refer to the future rather than to the present."
Source: Summa Theologica (New Advent)