The Rebbe stated that as soon as a bochur reaches the age of Bar Mitzvah, he should don both the Tefillin of Rashi and Rabbenu Tam.
(Si’ach Sarfey Kodesh II, 29. Rabbi Pinchos of Koretz stated that wearing the Tefillin of Rabbenu Tam is a segulah for cheshek to study pnimiyus ha-Torah; see Imrei Pinchos [Bnei Brak 2003] vol. I, Sha’ar Seder ha-Yom 38.)
The Rebbe wanted the Bar Mitzvah bochur to put on Tefillin for the first time on the morning of his thirteenth birthday, and not earlier. (If the birthday falls on Shabbos, he should don Tefillin on Sunday, not on Erev Shabbos.)
(Si’ach Sarfey Kodesh II, 30)