Likely true, but there are some unknowns:
Who wrote Ruth? She was not a Jew. Did she write it? [AF: She became a Jew by joining Klal Yisroel;no, it would be a Jewish man, by tradition Samuel the prophet]
Who wrote Job? His life came before the Jewish nation (I think). [af: Moses, by Jewish tradition, wrote Job
Who wrote Luke & Acts? Tradition often says he was a Gentile. Was he?[af: No. He was a doctor to the Jews, and an author of scripture. He was a Jew, albeit a Grecian (Hellenistic) Jew from the Diaspora. You may have popes who are not Italian, but all the authors of the oracles of God are Jews; not that the Gentile ECFs are not good reading; .............
More to my point, the Hebrew Scriptures were written before the early church came into existence.
And you didn't even ask who wrote Hebrews