Toward the very beginning of the Gemara is a well-known breisa:
אמר רבי יוחנן הרוצה לקבל עליו עול מלכות שמים שלימה יפנה ויטול ידיו ויניח תפילין ויתפלל
Translation: “R’ Yochanan said one who seeks to accept upon himself the yoke of the Kingdom of Heaven in a complete manner should empty his bowels, do the ritual hand-washing, lay tefillin and recite the prayers” (Brachos 14b).
Some readers might have noticed that something seems to be missing from the list: What about the mitzvah of tzitzis? Shouldn’t he put on a tallis?
This breisa is quoted by the Tur (O.C. 2, 6) in his description of how one should conduct himself upon rising in the morning. The Bach comments on the apparent omission, suggesting several possible explanations. His third suggestion reads as follows:
תפילין שבראש שאדם משעבד לבורא יתברך שהנשמה שהיא במוח וכו’ הני יש
ענין לקבלת עול מלכות שמים, מה שאין כן בציצית שאינה אלא לזכור את כל מצות ה
Translation: “The concept of tefillin on one’s head is to subjugate the mind to the Creator, for the soul is in the mind; yet this does not apply to tzitzis, which is merely to remember Hashem’s mitzvahs.”
Merely to remember Hashem’s miracles?! That’s no small matter! Apparently then the mitzvah of tzitzit is sort of a starting point. It makes you acutely aware of the deeds Hashem wants and expects of you, and serves as a constant reminder. This may explain why we put on the tallis before laying tefillin.
The Bach (O.C. 8, 1 s.v. Umiyad achar) writes that we put on tzitzis before tefillin because tzitzis are worn as a constant reminder of the mitzvahs, whereas the mitzvah of tefillin is primarily during Krias Shema and prayers, in order to accept upon himself the yoke of the Kingdom of Heaven in a complete manner.
Thus the act of donning tzitzis is a prelude to the process of accepting the yoke of Heaven.