Weren't arranged marriages still the common practice? At what age would a male be wed? Are their any sources that say when Jesus quit his earthly occupation?
Yes they were arranged. Sirach tells fathers to 'choose wives for them while they are still young' (7:23) cf 4 Esdras 9:47 where he also chooses a wife for his son. Women were married off as quickly as possible after menses, as they were seen as a burden and a potential liability on your honour, so puberty is normally the terminal point. Men should be married around the age of 18, as R Judah ben Tema says in m. 'Abot 5:21
He used to say: At five years old [one is fit] for the Scripture, at ten years for the Mishnah, at thirteen for [the fulfilling of] the commandments, at fifteen for the Talmud, at eighteen for the bride-chamber, at twenty for pursuing [a calling], at thirty for authority
Rabbinic literature indicates that men should be married as a religious obligation:
No man may abstain from keeping the law Be fruitful and multiply, unless he already has children: according to the School of Shammai, two sons; according to the School of Hillel, a son and a daughter, for it is written, Male and female created he them (Yebam 6.6)
So most would have been married. However, Joseph is normally understood to have been dead by the age of 12 (as he no longer figures in the stories), so he wouldn't have been around to organise Jesus' marriage anyway (this whole line is speculative on the texts).
However, there are plenty of examples of people who married late. Josephus was at least 30 before he was married, R Akiba was (perhaps legendarily) 33 before he was married, Eliezer ben Hyrcanus was in one text 28 and not married (but 22 in another), Rab Judah was criticized for not arranging a marriage for his Rabbi son, Levi in the Testament of Levi was married at 23 and his daughter married when she was 30, so while the texts are very pro-marriage, and pro-early marriage, it's not uncommon for people to marry late. It is important to note that many of our texts are pre or post the destruction of Jerusalem, so our 1st century sources are very small.
Jesus quit his earthly occupation at the age of 30, and quit this earth 3 years later (probably between 30-36AD)