Many languages distinguish between inclusive and exclusive first-person plural pronouns (“we”). 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 (“our father Jacob” in English translations), translators often select the inclusive form, whereas for the second part (“gave us this well” in English translations) the exclusive form.
Source: Velma Pickett and Florence Cowan in Notes on Translation January 1962, p. 1ff.
The Yagua translators (who, along with the translations into Malay, Sundanese, and Balinese, chose the exclusive for both parts of the verse) justify this by saying “Our choice here is exclusive assuming that the Samaritan woman to maintain the independent and factious spirit which this account shows existed between Jews and Samaritans.”
Source: Paul Powlison in Notes on Translation with Drills, p. 165ff.
Another opinion on using the inclusive pronoun for this verse and the remainder of the story:
“The Samaritan woman, in my view, is trying to get the better of Jesus; she appeals to Jacob (v. 12) and to ‘our fathers’ (v. 20) as to authorities higher than Jesus. If this is true, then it was important for her to show that those authorities were acknowledged by Jesus also. Therefore, we can imagine her to have thought or said ‘Your and my ancestor’ (v. 12) or ‘ancestors’ (v. 20) — inclusive pronoun in both verses.
“As for the phrase ‘who gave us the well’, there is certainly much truth in the consideration: “Since the well was in Samaritan territory, presumably she would use the exclusive form.” Yet, the inclusive can be defended here also, I think. With the remark that Jacob and his sons drank from the well, she is pointing back to a time anterior to the present antithesis between Jew and Samaritan; the well was given to ancestors of both peoples. Moreover, she comes to fetch water from the well and Jesus hopes to quench his thirst with its water. “The well is of common interest for both you and me,” she may have meant. It seems possible to find a third appeal to higher authority in v. 25. The woman has acknowledged Jesus as a prophet, but to the Messiah even a prophet has to bow; he, the prophet, as well as she, will have to be shown all things by the Messiah. Accepting this interpretation, we again have to use the inclusive ‘we’, Yet there is a difference with the verses first mentioned. In v. 12 and v. 20 the pronominal first person plural was used in phrases connected with the past; v. 25 points to the future, to the time when the Messiah will come and teach. A consciousness among the Samaritans of a Messianic belief common to both Jews and themselves is a necessary presupposition of the interpretation of v. 25 given above. So we are led to the preliminary question whether such a consciousness existed in Jesus’ times.”
Source: J. L. Swellengrebel in The Bible Translator 1959, p. 37.