הלכה על ברכות 18:35

The morning Tamid could be brought starting from dawn (“amud ha-shaḥar,” when the first light appears in the east), and the time for praying Shaḥarit should begin at dawn le-khatḥila. Nonetheless, the Sages said that it is proper to recite the Amida after sunrise (“hanetz ha-ḥama”), as it is written: “They shall revere You along with the sun” (Tehilim 72:5; Berakhot 9b). Be-di’avad, if one recites the Amida after dawn but before sunrise, she fulfills her obligation because she prayed at the time when the morning Tamid offering was brought (SA 89:1; and see Peninei Halakha: Prayer, ch. 11 n. 4). The most praiseworthy time to pray is when the early saints, the “vatikin,” who would recite the Amida at the moment of sunrise to fulfill “They shall revere You along with the sun.”¹There are various opinions about the precise time of amud ha-shaḥar, and they are detailed in Peninei Halakha: Prayer, 11:2 n. 1. As a rule, amud ha-shaḥar is never less than 72 minutes before hanetz ha-ḥama. Meaning, by the time it is 72 minutes before hanetz ha-ḥama, amud ha-shaḥar has definitely already occurred.
It is important to know that the earliest time for all daytime mitzvot, such as shofar blowing and brit mila, is sunrise, because the day is defined by the presence of the sun. However, be-di’avad if such mitzvot are performed from the time of amud ha-shaḥar, one’s obligation is fulfilled, because from a certain standpoint, the day begins from first light (Megilla 20a).

The time for putting on tefillin is like 'Others" in Berachot 9. One should wear them all day, and even to do business in them is permitted, and snacking is also permitted. But idle activities are prohibited. If one is worried this seems haughty before other people, one may wear only the hand tefillin. In any case, it is better to wear a small head tefillin and keep the straps covered than to walk with only the hand tefillin.