We know Carnelius was a just man who actually received the sacrament at the hands of St. Peter himself. That much we know.

"Because he did not know such a thing as baptism existed, he could not have desired it,

but because he was a just man, God provided it

- He sent St. Peter to baptize him because after the promulgation of the Gospel, without the sacrament, even a just man could not have entered the kingdom of God - per God's own divine revelation in John 3:5.

See how God's Providence works?

Trent doesn't interpret John 3:5 like that. It interprets John 3:5 in the context of justification i.e. becoming just.

1) We refer again to Father Deery’s letter, quoted above, to note its conclusion. Bishop Harrington and he had previously made a special trip to Rome to discuss our case with the Holy Office. What Father Deery wrote here, then, amounts to the Bishop of Worcester advising the Archbishop of Boston about the current attitude of the Holy Office regarding the Father Feeney case and the Crusade of Saint Benedict Center:

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It would seem that the Congregation for the Doctrine of the Faith holds the doctrine to
have been defined and consequently definitive. It is its theological interpretation and
speculation which they see as problematical.

In our discussions with the Congregation it seemed rather clear that proponents of a
strict interpretation of the doctrine should be given the same latitude for teaching and
discussion as those who would hold more liberal views.

We ask Father Laisney: If a proposition prefaced with the words "Amen, amen, I say
to thee," is not to be taken literally, then which of Our Savior’s words were so
intended?

Individual theologians may have tampered with the meaning of Christ’s words, but
the Church has never taken them to mean anything other than what they clearly
say.

Here are some popes and saints speaking on the principles of interpretation:

Saint Alphonsus Maria de Liguori: "The inspired writings have different senses,
namely: the literal and mystical. The literal sense is that which the words plainly
signify, and this sense alone supplies proofs of faith. The mystical sense never
affords proofs of faith unless confirmed by another text which explains the passage
in conformity with the mystical sense, or when the Fathers commonly agree in
expounding it in the mystical sense." (An Exposition and Defense of all the Points of
Faith Discussed and Defined by the Sacred Council of Trent)

Saint Teresa of Avila: "All the evil in the world comes from ignorance of the truths of
Holy Scripture in their clear simplicity, of which not one iota shall pass away." (The
Great Commentary, Father Cornelius a Lapide, S.J.)

Pope Benedict XV: ". . . all interpretation rests on the literal sense." (Encyclical
Spiritus Paraclitus)

Saint Thomas Aquinas: "It is not lawful to add anything to the words of Holy
Scripture regarding the sense, for all the senses of Sacred Scripture are founded on
one — the literal sense — from which alone can any argument be drawn." (Summa
Theologica, I, q.1, art.10, ad 1)

Pope Leo XIII: In his Encyclical On the Study of Holy Scripture, the Holy Father
quotes Saint Augustine’s admonition "not to depart from the literal and obvious
sense except only where reason makes it untenable or necessity demands."

The above references are taken from an excellent little booklet, Credo —
Foundations of Faith, written and published by Michael Malone, whom we quoted
earlier. With his permission, we quote further from the conclusion of his section on
the interpretation of Holy Scripture:

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St. Alphonsus Maria continues his comments above in affirming that "we must believe
with the certainty of faith not only what has been defined by the Church, but also what
appears to be clearly contained in Scripture; otherwise, everyone might doubt of any
truth expressed in the Sacred Writings before the definitions of the Church."

It follows, then, that we are bound to hold to the literal meaning of all the doctrinal or
moral truths found in Holy Scripture, even before they are defined by the Church. For
example, every soul among the faithful professed belief in the necessity of the
Sacrament of Baptism for eternal salvation during the fifteen centuries prior to its
definition by the Council of Trent in its seventh Session of March, l547, based on the
clearly literal words of Jesus Christ Himself to Nicodemus as recorded in Saint John’s
Gospel (3:5).

The faithful have also held from the very beginning that the true and total Faith is
required of all the Elect, as Our Lord declared: "He who believes and is baptized shall
be saved; he who does not believe shall be condemned" (Mark 16:16). Furthermore, no
Catholic is free to hold any teaching which might serve to contradict these literal
expressions.

This principle concerning the literal interpretation of Holy Scripture is at the very
heart of Father Feeney’s opposition to the wild misuse being made today of the
term "baptism of desire."

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He sent St. Peter to baptize him because after the promulgation of the Gospel, without the sacrament, even a just man could not have entered the kingdom of God - per God's own divine revelation in John 3:5.

Trent doesn't interpret John 3:5 like that. It interprets John 3:5 in the context of justification i.e. becoming just.

Trent says, since the promulgation of the Gospel, per John 3:5 no one is justified without Baptism or its Desire.

Pope Paul III, The Council of Trent, Can. 2 on the Sacrament of Baptism, Sess. 7, 1547, ex cathedra:  “If anyone shall say that real and natural water is not necessary for baptism, and on that account those words of Our Lord Jesus Christ: ‘Unless a man be born again of water and the Holy Spirit’ [John 3:5], are distorted into some sort of metaphor: let him be anathema.”