Our Gemara on Amud Beis discusses the status of a child born from a Gentile father and Jewish mother. The child is not a halakhic mamzer but is seen to be of inferior lineage and cannot marry into the priestly families.

This would seem to be contradicted by the following verse in Vayikra (24:10):

וַיֵּצֵא֙ בֶּן־אִשָׁ֣ה יִשְׂרְאֵלִ֔ית וְהוּא֙ בֶּן־אִ֣ישׁ מִצְרִ֔י בְּת֖וֹךְ בְּנֵ֣י יִשְׂרָאֵ֑ל וַיִּנָּצוּ֙ בַּֽמַּחֲנֶ֔ה בֶּ֚ן הַיִּשְׂרְאֵלִ֔ית וְאִ֖ישׁ הַיִּשְׂרְאֵלִֽ׃

There came out among the Israelites a man whose mother was Israelite and whose father was Egyptian. And a fight broke out in the camp between that Son of the Jewess and a Jewish Man.

The son of the Jewish woman is not referred to as a Jewish person, while his Jewish opponent is directly called a Jewish Man. This implies that this son from an Egyptian man was not considered fully Jewish. Even more puzzling, Ramban (ibid) also quotes a Toras Cohanim that says he converted. Therefore, Ramban holds that this was not an issue of him being technically Jewish but rather a subtler matter of status. His lineage was not pure; he had no share in the Land of Israel because that comes from the father, and his father was Egyptian. Thus, the verse is describing a man who wanted to be part of the Jewish people, even "converted," not in the halakhic sense but in the sense of committing to mitzvos. Unfortunately, he became disillusioned, because he did not feel that he was treated as Jewish in that he would not have a birthright in the Promised Land.

The Chokhmei Tzarfas (brought down in Ramban ibid) argue and say that he did have to convert for real,because prior to the covenant at Mount Sinai, all Jews had a halakhic status of a gentile. Now regarding lineage of two gentiles who have a child, we follow the father, and so the child was not really Jewish at all until he converted, because even the mother did not yet have a fully Jewish status prior to Mount Sinai. Ramban objects strongly to this, stating that Avraham was the first convert, and his children had the status of Jews. This is, even to the extent that Esau was considered Jewish (albeit an apostate, but still Jewish. See Kiddushin 18a).

What is the underlying principle that is in dispute between the Chokhmei Tzarfas and Ramban? We can frame it as being about what makes Jewishness. It would seem the Chokhmei Tzarfas hold that without the covenant at Mount Sinai, Jewishness does not exist. No Torah, no Jews. According to Ramban, Mount Sinai and the mitzvos are additional covenantal obligations, but Jewishness began with Abraham. What is the nature of this Jewishness according to Ramban? Gentiles also could have been monotheistic in Avraham’s time, and for that matter, in ours. It seems, the fact of being chosen and entering the initial covenant of the Bris Milah makes Avraham and his descendants Jewish. I don’t know if there is a practical difference between these two opinions, but metaphysically it is significant. According to Ramban, the Torah is something Jews agreed to do, but they are Jews independent of that via the Bris Milah covenant. According to the Chokhmei Tzarfas, the Torah IS being Jewish, not just a feature of Jewishness.