Wouldn’t this mean that faith is what justifies** and baptism is the sign and seal of the ‘righteousness one has by faith’?
It’s not either-or. It’s both of them as a singular thread of faith. For example:*
Of this Justification the causes are these: the
final cause indeed is the glory of God and of Jesus Christ, and life everlasting; while the efficient cause is a merciful God who washes and sanctifies gratuitously, signing, and anointing with the holy Spirit of promise, who is the pledge of our inheritance; but the
meritorious cause is His most beloved only-begotten, our Lord Jesus Christ, who, when we were enemies, for the exceeding charity wherewith he loved us, merited Justification for us by His most holy Passion on the wood of the cross, and made satisfaction for us unto God the Father;
the instrumental cause is the sacrament of baptism, which is the sacrament of faith,
without which (faith) no man was ever justified; lastly, the alone
formal cause is the justice of God, not that whereby He Himself is just, but that whereby He maketh us just, that, to wit, with which we being endowed by Him, are renewed in the spirit of our mind, and we are not only reputed, but are truly called, and are, just, receiving justice within us, each one according to his own measure, which the Holy Ghost distributes to every one as He wills, and according to each one’s proper disposition and co-operation. (
Council of Trent, 6.7)
*So you see the continuity in baptism and faith. The plural “causes” are really a singular concept, not one vs. the other. It’s kind of like asking did Jesus save us by his suffering, his death, or his resurrection? The answer is rather his entire Passion, which encompasses all these. Likewise, when James analyzes faith and works, he sees them as a singular unit, comparable to a body
and spirit making up a singular living person (Jam. 2:26). And likewise, baptism is not an opponent of faith, but its “personification,” so to speak.
Another way to think of it is the sacrament of confession. Some people think that forgiveness “occurs” as soon as the person repents, and therefore doesn’t “need” to go to confession. Rather, confession is the continuation of a singular repentance (followed by satisfaction). To reject the latter is to destroy a multi-faceted repentance that is irreducible. Similarly to justification, to amputate baptism is to destroy a faith that is irreducible without baptism.