Here's something I've got no idea about. In the case where one party is married in a Baptist Church but divorced and the other party has no encumbrances. Barring quarrelsome arguments I can't answer concerning grounds for annulment, is the first party even required to do anything to prove that their first marriage is null and void?
Code of Canon Law Can. 1060 Marriage possesses the favor of law; therefore, in a case of doubt, the validity of a marriage must be upheld until the contrary is proven.
Thus the Church recognizes the marriages of non-Catholics as well and considers them valid until proven otherwise.
Answering assuming the party with no encumbrances is Catholic
No marriage can occur until the marriage of the party previously married in the Baptist Church and now divorced is examined by the Church and a decree of nullity issued (i.e. in the eyes of the Church, that marriage never existed to begin with).
Once that decree has been issued, the requirements for a mixed marriage must be met for there to be a valid marriage in the Catholic Church.
Why does the Catholic Church require an intended spouse, who is divorced but not Catholic, to obtain an annulment before marrying in the Catholic Church?
The Catholic Church respects all marriages and presumes that they are valid. Thus, for example, it considers the marriages of two Protestant, Jewish, or even nonbelieving persons to be binding for life. The Church requires a declaration of nullity to establish that an essential element was missing in that previous union preventing it from being a valid marriage.
This is often a difficult and emotional issue. If the intended spouse comes from a faith tradition that accepts divorce and remarriage, it may be hard for them to understand why they must go through the Catholic tribunal process. Couples in this situation may find it helpful to talk with a priest or deacon. To go through the process can be a sign of great love of the non-Catholic for their intended spouse.
It is my belief that the following are also pertinent: