I am not certain whether your question is based on the fact that a Get must be written before it can be given, or whether it is because the Pasuk puts writing it first: "ve'kasav Lah Sefer Kerisus ve'Nasan be'Yadah". We do find a number of Masechtos where Rebbi follows the chronological order of events, such as Pesachim and Yoma. Tosfos, on the other hand, ask at the beginning of Shabbos, why Shabbos appears not to follow a chronological order (as it begins with the Lav of Hotza'ah, which pertains to Shabbos itself, rather than with the Dinim of Erev Shabbos, which it deals with later). And they explain that it is either because Rebbi preferred to begin with the Dinim of Hotza'ah, since we learn such a variety of Halachos from it, or because Hotza'ah is extremely common, and it is customary to begin with that which is most common.

In any event, we see from Tosfos that although, Lechatchilah, it is ideal to start from the beginning, as it were, and to follow the chronological order, a small motive might well suffice to waive that prerefernce. It seems that here too, Rebbi for some reason preferred to begin with the giving of the Get (perhaps it is the Ikar Mitzvah, whilst writing it is only a Hechsher [a preparation of the Mitzvah]).

be'Virchas Kol Tuv

Eliezer Chrysler