First things first, Star Wars: Dawn of the Jedi series deals with the Je'daii Order, the order directly preceding the Jedi Order but not considered the same body. The Order of Dai Bendu preceded the Je'daii Order and could be said to be its spriritual ancestor.
1. The Order of Dai Bendu = at least 37,453 BBY - 36,453 BBY
One of the earliest groups to discover the Force, a millenia before the formation of the Je'daii Order they discovered a pyramidal edifice they could "hear". They called it the "Tho Yor", and tended it for a thousand years, before it "woke up" and revealed itself to be a starship, which transported them to the world of Tython, where they contributed to the foundation of the Je'daii Order.
2. Je'daii Order = 36,453 BBY - 25,783 BBY
Wookiepedia gives the date of formation of the Je'daii Order as 36,453 BBY, sourced to Star Wars: Dawn of the Jedi: Force Storm 1 (the first issue of the Dark Horse miniseries)
The Monks of Dai Bendu had been only one of eight Tho Yor, that had repeated the pattern elsewhere in the galaxy, gathering Force-sensitive sentients who could hear their call and bringing them to Tython. These force-sensitives became the first Tythans and together became the Je'daii Order.
The collapse of the Je'daii Order came about due the Force Wars - the conflict between Dark-side (Bogan) and Light-side (Ashla) followers in the Je'daii Order. And post-war, the surviving Light-Siders led to the formation of the Jedi Order.
3. Jedi Order = 25,783 BBY - 19 BBY
Wookiepedia gives the date of formation of Jedi Order as 25,783 BBY, sourced to SWTOR Timeline Video 1. It seems to the the date of the end of Force Wars, one of the direct outcomes of which was the creation of the Jedi Order.
The Je'daii philosophy had been balance between Ashla (Light side) and Bogan (Dark side). However, after the Force Wars, when the followers of Bogan were defeated, the victors, i.e. the followers of Ashla abandoned the philosophy of balance, stating the Light side to be stronger and this splinter group began calling themselves Jedi and formed a Jedi Council consisting of the founding members: Jedi Masters Rajivari, Garon Jard, Cala Brin and Ters Sendon. (Rajivari later abandoned the Light, and could be said to be the first Dark Jedi)
This organization persisted until the Great Jedi Purge led by Darths Sidious and Vader in 19 BBY, though it almost perished with the First Jedi Purge during Darth Revan's time in 3954 BBY.