//No man is Justified by the "laver of regeneration" if he does not have the "desire thereof". No man is Justified by the "desire thereof" if he does not have the "laver of regeneration"//
What about infants?
As others have pointed out, that section is about adults, not infants. There's a Canon in Trent rejecting the notion that the Sacrament justifies even if the recipient has no intention to receieve it.
What Trent is actually teaching here simply addresses the Protestant heresies, things like how Catholics, believing the Sacraments operate
ex opere operato have a superstitious or magical view of how they work ... which is why in the entire Treatise on Justification, the narrative is geared toward explaining the COOPERATION of grace and free will in the process by which the Sacrament justifies. That's a strong reason to consider that the "laver" and "votum" section does in fact truly mean that both are requred and that there's no justification without one or the other, meaning not without one or else the other (the word "saltem" could have been used, or the conjunctive "or", "vel" rather than "auth".
I used to believe that Trent taught BoD here, but then I read the ENTIRE Treatise on Justification, and the context makes it clear what the intent of the teaching is, to explain the cooperation of "ex opere operato" effect of the Sacrament and unmerited grace, with the cooperation of the subject who is justified.
So that when you get to the "laver" or "votum" section, it would be absurd to say, after all that, Trent says and adult can be justified with EITHER the laver OR the votum, when everything leading up to it, the whole point of it was that both are necessary. And that's to say nothing of the proof text Trent cites immediately after the "laver" or "desire" section, namely, where Our Lord taught that water AND the Holy Ghost are necessary to be born again, with water being the "laver", the Sacrament, and the "votum" being analogous with the role Our Lord taught the Holy Ghost held, to inspire that cooperation, that "votum".
"We cannot have the wedding without a bride or a groom."
"I cannot write a letter without a pen and paper."
"I cannot write a letter without a pen or a pencil."
In the first two it's clear that both are necessary and that if either one is missing you can't have the wedding. In the third one, it's clear that one OR the other suffices, where I can write a letter with either a pen or a pencil.
Let's say I have never heard of or seen baseball and someone says, "We cannot play baseball without a bat or a ball." So, which type of construction is this? I can't tell unless I know about baseball. It's ambiguous. But now, what if someone says, "We cannot play baseball without a bat or a ball, since you need a bat and a ball to play baseball." Now the meaning is clear.
Let's look at Trent then:
"Justification cannot happen without the laver or the desire ..." (is it one or the other, is it both?)
How about now ?
"Justification cannot happen without the laver or the desire, since Our Lord taugth that we must be born again of water AND the Holy Ghost."
Clearly Trent is making an analogy, like those old SAT tests. laver:water::votum:Holy Ghost, read as "laver is to water what votum is to Holy Ghost". That's why Trent adduces this as a proof text.
But to read it the standard way, one would have to say that this ... "We cannot play baseball without a bat or a ball, since Bob told me we need a bat and a ball in order to play." ACTUALLY MEANS that we can play baseball if we just have one or the other.
Now, another problem with the either ... or reading.
Justification cannot happen without the laver or the votum.
If by this you mean either ... or, then the logical corollary is that "Justification CAN happen without the votum." (but that's condemned, where Trent teaches that the Sacrament doesn't justify without the votum) and that "Justificiation CAN happen WITHOUT the laver." That's also a huge proble, since Trent clearly taught that justification cannot happen WITHOUT the Sacrament, so Trent would be contradicting its own teaching. Even in a BoD type of scenario, you have to say that the Sacrament of Baptism is still necessary, i.e. that justification cannot happen WITHOUT it, just that somehow it operates through the
votum or, as St. Robert Bellarmine said, it's not that we do not receive the Sacrament, but that we receive it
in voto, where it's more an alternative mode of receiving the Sacraement. He developed this forumulation precisely because he realized that it would be heretical to say someone can be justified without the Sacrament.
Finally, another reason that after I read the entire Treatise I changed my mind about my prior belief that Trent taught BoD is ... where is any mention of Baptism of Blood? If Trent were teaching or intending to teach about the so-called "Three Baptisms", then why silence about the BoB? According to the theorists, like St. Alphonsus, BoB has a "quasi-ex-opere-operato" effect, where it does remit all temporal punishment due to sin (unlike BoD), so it does not simply reduce to BoD. If you read Trent the way BoDers do, you have to reject the notion of a BoB that's in any way distinct from or does not reduce ultimately to BoD ... where one is justified by the Baptism of Desire, and then maybe BoB is just an add-on of sorts to wipe out temporal punishment due to sin.
None of the BoDer position makes any sense, not if one actually sits down and reads the Treatise on Justification with an open mind and in the original Latin if possible, since English translations can be misleading, and one of the most popular ones represents a DELIBERATE mistranslation to force BoD thinking into those passages.