I touch the box with my strap and kiss the box (shel yad and shel rosh).
If you take the Shel Rosh first, you must cover it up and put the Tefillah Shel Yad first. You are not passing over the mitzvah becasue the pasuk says: U’Kshartam Le’Ot Al Yadecha Vehayu LeTotafot Ben Eineikha which is darshened (1) the order is the hand and then the head and (2) Totafot is plural of Ot which means that you have to “see two Ot” at the time of the head tefillin; i.e., one on your hand and the second on the head. Also, there is a halakhic rule of Ma’alin B’Kodesh V’Ein Moridin which means that you increase in Kedusha but not decrease. Since the Kedusha of the Rosh Tefillin is greater than the Kedusha of the Yad Tefillin, we place the Yad Tefillin first.
All this is under the consideration that there are no injuries to your arm, etc… If that is the case, you must consult your Local Orthodox Rav.