Well, Dave,
I work with marriage cases at a tribunal. Perhaps this will help.
Bear06 gave you the absolutely correct answer: the tribunal will indicate how to proceed. I can only add a fuller picture of the concept.
A Catholic cannot validly marry a non baptized party without a dispensation from disparity of cult (c. 1085).
If a non baptized party concealed the fact of non baptism, it is possible that no dispensation was sought. Sometimes though, the dispensation is sought anyway as a caution (ad cautelem).
The prenuptial records and the chancery archives will be examined to clarify whether it was given or not.
If there was no dispensation and it was needed, there is still a tribunal process, called the documentary process of canon 1686: “When a petition has been received in accord with can. 1677, the judicial vicar or a judge designated by him, omitting the formalities of the ordinary process but having cited the parties and with the intervention of the defender of the bond, can declare the nullity of a marriage by a sentence, if from a document which is subject to no contradiction or exception there is certain proof of the existence of a diriment impediment or a defect of legitimate form, provided that it is clear with equal certitude that a dispensation was not granted; this can also be done if there is certain proof of the defect of a valid mandate of proxy.”
However, it is a much simpler process and although it is a nullity of marriage case, some things are different. Usually it does not involve the writing of testimony, since the proof of nullity is established by documents. Witnesses are not cited as a rule. The case does not have to wait for publication of the acts.
This process does not require mandatory review by a second tribunal, and as a defender of the bond, I do not recall ever having to appeal one of these cases, nor of a responding party ever making appeal.
As a matter of information, if prenuptial proof of baptism could not be obtained with certainty by a document or witnesses other than a prospective bride or groom, it would be customary in most places, to have sought the dispensation ad cautelam.
If this were done, then the full process would need to be followed.
But, only your tribunal knows…