Answer: The Shulchan Aruch (OC 37:3) writes that a boy’s father must buy him tefillin when he’s mature enough to control himself and treat them with the proper respect. R’ Ovadia Yosef (Yabia Omer OC 6:3; Yechave Daas 2:4) demonstrates that this is the sefardi minhag (See Ohr Letzion 2:44:47)
While the Rema disagrees, writing that he must wait until he’s bar mitzva, the Magen Avraham (37:4) and Shulchan Aruch Harav (OC 37 write that the minhag is for boys to start wearing them two or three months before their bar mitzva. Thus, minhag chabad is for boys to begin wearing tefillin two months before their bar mitzva.
The Aruch Hashulchan (OC 37:4) notes that the minhag ashkenaz is to begin one month before one’s bar mitzva. R’ Eliezer Waldenberg (Tzitz Eliezer 13:10:3) notes that this is the minhag ashkenaz in Yerushalayim. He adds that even though they are doing so to train themselves for when they are bar mitzva, they should still say a beracha.
R’ Waldenberg later (ibid. 13:24:5) writes that one who who wears them in advance of his bar mitzva doesn’t recite shehecheyanu as when he first wears them, he does so to train for when he is bar mitzva and later on they are no longer new. Yet, the Chasam Sofer (OC 55) suggests that a bar mitzva boy recites shehecheyanu when he wears his tefillin for the mitzvos that he is now obligated.
As there is a doubt as to whether one should say shehecheyanu or not, the Mishna Berura (Biur Halacha 22:1) recommends that one wears new clothing then so that one says shehecheyanu on both simultaneously. Similarly, R’ Shlomo Zalman Auerbach (Halichos Shlomo 4:14) ensured that while his sons began wearing tefillin a month before their bar mitzva, he didn’t gift them their tefillin until the day of their bar mitzva so that they could say shehecheyanu then.
In conclusion, the main ashkenazi custom is for boys to begin wearing their tefillin for a month before their bar mitzva with a beracha. Ideally, they should wear a new suit on their bar mitzva and recite shehecheyanu when they put on their tefillin.