The earliest time to Daven Shacharis – Summary:^[1]

The start time-From when in the morning may one daven the Shacharis Shemoneh Esrei?

Neitz/Sunrise-Lechatchila/The initial time: The ideal time for praying Shemoneh Esrei is exactly by sunrise, [unless a minyan is not available at that time, or if Davening this early will compromise on one’s Torah learning schedule, or ability to concentrate in the prayer, in which case one may Daven later on]. Thus, one should not Daven Shemoneh Esrei before sunrise unless it is a time of need. 

Mi Sheyakir and Alos-Time of need and Bedieved: In a time of need, it is permitted for one to Daven Shacharis prior to the time of sunrise, but after Mi Sheyakir, and in certain extraordinary cases it is permitted to Daven Shacharis even prior to the time of Mi Sheyakir but after daybreak/Alos. In all cases, Bedieved, if one Davened Shacharis from after daybreak [but before sunrise], then he has nevertheless fulfilled his obligation.

Cases of need in which praying before sunrise is permitted:

Traveling before sunrise: If one must travel out of the city prior to sunrise and will be unable to Daven afterwards while standing, then one may pray the entire prayer before sunrise. [Thus, if one must take a bus or flight prior to sunrise which will continue until after Zeman Tefila, then he may pray the entire Shacharis prior to sunrise after the time of Mi Sheyakir.]

Must begin work prior to sunrise: If one begins work very early, near sunrise, then he is to Daven before going to work. This applies even if he will have to Daven alone before sunrise without a Minyan. Certainly, it is permitted for a group of men who go to work before sunrise to arrange a daily Minyan prior to sunrise.

No Minyan after sunrise: If the only available minyan is before sunrise, then it is better that one Daven with the Minyan before sunrise than to Daven alone after sunrise.

One suspects that he may miss Zeman Tefila:  In any case that one suspects that delaying his prayer past sunrise may cause it to be delayed until after Zeman Tefila, then he may precede to Daven prior to sunrise.

The order of prayer when praying prior to sunrise:

Before Alos: One may recite all the morning blessings that he became obligated in, and may recite Mah Tovu etc, up until the paragraph of Terumas Hadeshen. In the winter, he may recite also the paragraph of Terumas Hadeshen prior to Alos.

After Alos but before Mi Sheyakir: One may recite all the Karbanos, as well as Pesukei Dezimra without Tallis and Tefillin.

From Mi Sheyakir: One may put on Tallis and Tefillin and recite Shema and Birchas Shema and Shemoneh Esrei.

[1] See Admur 89:1-2; Michaber 89:1; Rambam Tefila 3:1; Mishneh Brachos 4:1; Ketzos Hashulchan 20:1; Piskeiy Teshuvos 89:2-5