The custom regarding at what age to start wearing a tallit can be somewhat puzzling. Some young men start wearing a tallit when they reach the age of bar mitzvah, while others wait until they get married. Why the discrepancy?

The Magen Avraham cites a passage of the Gemara that indicates unmarried men did not cover their head with the tallit, and the Maharil writes that the custom is not to wear a tallit at all. The reason given is that the Torah writes the mitzvah of tzitzit immediately after the mitzvah of getting married, showing that this is the order in which they are meant to be fulfilled (see Devarim 22:12-13). However, Sefardim and many communities in Western and Central Europe did wear a tallit before marriage, because they did not view the above interpretation as halacha to be carried out in practice.

Thus today, most Ashkenazi yeshiva students do not wear a tallit before their wedding at all; Sephardic yeshiva students (and a minority of Ashkenazim as well) do wear a tallit gadol, but never pull the tallit over their heads.

Strictly speaking, the only requirement is to wear tzitzit on a four-cornered garment (i.e. a tallit katan), whereas the tallit gadol as we know was not originally mandatory, rather a custom evolved to wear a tallit during Shacharit. This custom may be even more important for those who do not wear tzitzit all day, since without a tallit they would be “testifying falsely” when they read the passage about tzitzit in Kriat Shema. (Notably, the Tosafot argues that this applies to tefillin, but not to tzitzit.)

In certain communities, notably German Jews and Yemenite Jews, even young boys wear a tallit in shul.

Further Resources:

Tallit Before Marriage
Tallit Gadol for Unmarried Individuals