I seem to recall a Jewish sage saying of the Pharisees, "you travel around by sea and land to make one proselyte" (Mat. 23:15). Also, Josephus mentions in
Against Apion that in every city there were large numbers of Gentiles who took on the Torah, up to an including the kosher laws, in every city. Rabbi Hillel (who died when Yeshua was about 7-15) was known in the Talmud for encouraging proselytes; presumably his disciples were as well.
So yeah, Judaism was at one point a missionary religion. Roman and then Christian persecution put a stop to that, causing the Jewish community to turn inward instead.
Shalom.