When did the tradition of bar mitzvah begin?
Depending upon what you mean by "tradition":
- from the time of Abraham, by 1st century BCE, or 16th century CE.
The period of the Torah when Abraham feasted the coming of age of Issac
The feast of the weaning of Issac is sometimes given as the origin of the bar mitzvah. Note that this "weaning" is generally regarded as figurative; the time when Issac became a religiously responsible adult, subject to taxation and military service (at age 20).
By period of the Talmud (at some point prior to 1st century CE) when the age of maturity was set at 13
By the time of the final codification of the Talmud, the age of becoming bar mitzvah was set at 13.
(from within Germany/Poland) males gained the rights and obligations (at age 13) within the synagogue during the 16th century CE
During the Middle Ages, within Europe, religious participation of children was seriously curtailed. Only at age 13 were boys allowed religious obligations and rights. During the 1600's (CE) this gradually became the bar mitzvah celebration.
I am not Jewish; this is strictly my understanding based on
admittedly limited memory of Jewish history.
Perhaps someone from within the Jewish community would
care to expand upon or refute the above.