TT #24 · Parashas Va’eschanan · Passuk 6:8
And you shall bind them as a sign upon your hand, and they shall be for frontlets between your eyes.
Torah Temimah points to the classic sources for the order of donning tefillin (hand before head) and the requirement that the head tefillin not be worn without the hand tefillin (Menachos 36a and parallels).
English: “And you shall bind them as a sign upon your hand” — this is the hand tefillin. “And they shall be for frontlets between your eyes” — this is the head tefillin. From here we learn that one puts on the hand tefillin first and afterward the head tefillin.
Sequence from the order of the biblical phrases (hand before head).
Hand tefillin are donned before head tefillin; the order of the verse is the order of the practice.