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”).
According to Velma Pickett and Florence Cowan (in Notes on Translation January 1962, p. 1ff.) for this verse, translators typically select the inclusive form (including Cornelius and his relatives and friends).
According to SIL International Translation Department (1999), the exclusive could also be used since “the ‘we’ indicates the separation that existed between Jews (‘we’) and Gentiles (‘they’), beginning several thousand years before. Peter was amazed that God would give the same gift of his Holy Spirit to Gentiles that he gave to Jews at Pentecost.”