Many languages distinguish between inclusive and exclusive first-person plural pronouns (“we”). (Click or tap here to see more details)
The inclusive “we” specifically includes the addressee (“you and I and possibly others”), while the exclusive “we” specifically excludes the addressee (“he/she/they and I, but not you”). This grammatical distinction is called “clusivity.” While Semitic languages such as Hebrew or most Indo-European languages such as Greek or English do not make that distinction, translators of languages with that distinction have to make a choice every time they encounter “we” or a form thereof (in English: “we,” “our,” or “us”).
For the first part of this verse, translators typically select the exclusive form (excluding the addressee). For the second part (“our God” in English translations) the inclusive form is typically used.
Source: Velma Pickett and Florence Cowan in Notes on Translation January 1962, p. 1ff.
In Fijian the trial exclusive form “neitou” (“of me and of them two”) is used for the first part of this verse instead. This choice is understandable in view of the introduction found in both letters to the Thessalonians, where the writer Paul indicates clearly that the letters were co-authored by two other colleagues, Silas and Timothy, hence the use of a pronoun referring to three people (“Paul, Silas and Timothy”).
Source: Joseph Hong in The Bible Translator 1994, p. 419ff.