The dominant practical ruling is that one does not recite Shehechiyanu when putting on tefillin for the first time, because Shehechiyanu is reserved for a mitzvah that recurs from time to time, and tefillin, like other acquisitions-mitzvot, does not fit that category: so rules Kitzur Shulchan Arukh Yalkut Yosef, Orach Chaim 225:21 and Kitzur Shulchan Arukh Yalkut Yosef, Orach Chaim, חינוך קטן במצות תפילין 37:6, and Kaf HaChaim (Palagi) 10:8 states the same distinction, contrasting a new tallit — on which Shehechiyanu is said — with new tefillin, on which it is not.
This position traces to the view cited by Beit Yosef, Orach Chayim 22:1, who notes that while the Rambam explicitly requires Shehechiyanu on ciztit, he conspicuously omits tefillin from that list, a discrepancy the Beit Yosef flags as puzzling even as he brings the Rambam's broader principle in Mishneh Torah, Blessings 11:9 that any mitzvah which constitutes a personal acquisition, such as tzitzit, tefillin, or mezuzah, calls for Shehechiyanu at the time of its performance.
The Shulchan Arukh and Mishnah Berurah apply this acquisition-based logic concretely to tzitzit: one who acquires a tallit and makes tzitzit in it recites Shehechiyanu because it is no less than acquiring new vessels, as in Shulchan Arukh, Orach Chayim 22, and if the blessing was not said at the time of making the tzitzit it is said upon first wrapping oneself in it, with Mishnah Berurah 22:1-2 clarifying that the blessing nevertheless does not extend to covering the mitzvah itself, since the mitzvah is not one that recurs from time to time.
That same general concept of Shehechiyanu for a new garment or vessel, and of a berachah being warranted for life-cycle novelty, is rooted in Berakhot 54a:3, which records the blessing for a new house or new vessels, and is extended in Sukkah 46a:1 to one who fashions a lulav or sukkah for himself, reciting Shehechiyanu at the time of construction even though a separate mitzvah-blessing follows upon actual use.
Nitei Gavriel, Bar Mitzva, perek 36 records that the question of reciting Shehechiyanu on first putting on tefillin is itself a matter of dispute among authorities, with one opinion directing that the blessing, when said, be intended to cover all future mitzvot as well.
Az Nidberu 7:3 addresses this directly, noting that although some hold Shehechiyanu should be said on performing any mitzvah for the first time, the Biur Halachah's position is that even for tefillin the primary ruling is not to recite it.
Revavos Ephraim 7:13 takes up a related first-time tefillin question, explaining that when only the tefillin shel yad was initially available its blessing could be intended to cover the shel rosh as well, but once the shel rosh became available its own blessing must be recited, since the obligation is fundamentally comprised of two separate blessings.
Tzitz Eliezer 11:17 discusses the practice of increasing joy on the day a youth first dons tefillin and notes a custom applying specifically to that first wearing, as well as a local custom of beginning to wear tefillin during the month preceding bar mitzvah, as echoed in B'Mareh HaBazak Volume III 10:7 regarding donning tefillin with a blessing a month or more before the halachic bar mitzvah date.
Nishmat Shabbat vol 1:352 likewise takes up tefillin worn for the first time, drawing a comparison to the practice of women reciting Shehechiyanu upon first lighting candles, which it characterizes as mistaken according to the essential law.
Separately, the sources on the mechanics of the tefillin blessings themselves — Mishnah Berurah 25:15 on the intention required when donning tefillin and the blessing recited beforehand, Beit Yosef, Orach Chayim 25:5 on whether one or two blessings are said depending on interruption between the shel yad and shel rosh, and Shulchan Arukh, Orach Chayim 29 together with Mishnah Berurah 29:1 on the rule that no blessing at all is said upon removing tefillin — concern the ordinary tefillin blessings rather than Shehechiyanu, and the question in Rosh Hashanah 29b:1 about whether a blessing is obligatory likewise bears on the general category of blessing-obligation rather than on Shehechiyanu for a first-time mitzvah.
