Judaism spread in the ancient world primarily by

The Jewish ideology spread along with the physical scattering of Jewish people due to several instances of historical exile, including a diaspora, or scattering, at the hands of the Romans in 70 C.E. and a conflict with Assyrians in 722 B.C.E. In addition to the physical spread of the Jewish worldview along with the physical scattering of Jewish people at various points throughout history, Judaism has spread through proselytizing, or the preaching of one's religion with the aim of conversion. However, while proselytizing is not outright banned by the Jewish faith, historical hostility and intolerance of Jewish people by dominant religions has led to a lack of emphasis on this practice compared to some other religions.

i'd assume india mainly because of how isolated japan was.   plus it is a whole china away.