I'm continuing my way through Louis Feldman's Jew and Gentile in the Ancient World:
I have written about the prohibition in the Babylonian Talmud (Chagigah 13a; Sanhedrin 59a) on teaching Torah to Gentiles. Feldman states that Josephus was aware of this, and yet that Josephus asks if the Greeks have learned the history of the Jews and proceeds to talk about that history with a pagan audience in mind. I have also written about how the Gentile intelligentsia tended to view the Jews as anti-intellectual, as people who were unwilling to put their ideas out there in the realm of debate and to yield if they were proven to be wrong.
Although the Talmud later banned Jews from teaching Torah to the Gentiles (a rule that may have come before the Talmud), Jews sought to demonstrate that they had something to contribute intellectually. Philo said that the Greek philosopher Heraclitus stole the theory of opposites from the Torah. Josephus quotes the historian Hermippus, who lived around 200 B.C.E. and supposedly said that Pythagoras got ideas from the Jews, which made sense to some because Pythagoras condemned the use of images.
Then there was proselytism, which was rooted in the notion that the Torah (or Judaism) was for all peoples. Wisdom of Solomon 18:4 says that the law is light for the world, and the second-first century B.C.E. Testament of Levi (14:4) contains a similar idea. The second century B.C.E. Sibylline Oracles (3:5-10) says that all made in God's image should walk in the straight path, the oracle, which Jews should proclaim. Philo presents the conversion of Gentiles to the Torah as a journey from darkness to light, virtue, and holiness. Josephus in Antiquities 1:162-168 portrays Abraham as one who went to Egypt to persuade the Egyptians, and Josephus notes that Abraham was willing to change his mind if the Egyptians presented more compelling arguments. Joseph in Genesis Rabbah 90:6 and 91:5 refuses to sell grain to Egyptians who will not be circumcised. Not all of these items necessarily relate to the Gentiles embracing the Torah, but there was a view that the Torah or the religion of the Jews belonged to the marketplace of ideas and exemplified wisdom, which was for all peoples.