The X Continuum was supposedly created when several Q's branched off from the Q Continuum after one Q changed his name to X. But the actual state of this Continuum was never brought into existence until the duplicated omni'power within a Talarian named Rein was grown into omnipotence without the influence of the Q. (Star Trek: Phoenix-X)
In 2376, the Phoenix-X encountered a rogue Q, who escaped the Q Continuum and changed his name to X. He felt it unnecessary to live by their rules or to even go on - so he killed himself and gave his powers to the Captain of the Phoenix-X, Daniel. ("The X Continuum")
In 2377, more Q's from the Continuum had repeated X's actions (without the suicide aspect), and began changing their names to X. As rules were starting to begin, one of the X's came to visit Daniel. He receded Daniel's powers to a fraction, so that the Captain would instead learn to grow with his power - to the goal of one day joining a preconceived X-Continuum.
Daniel's powers were then limited to energy-expulsions and extra-sensory powers (these were along with his already Changeling shapeshifting abilities). ("Vengeance")
During this time, the X's themselves began recruiting mortal after mortal throughout the galaxy. This was a turning point in History, as they bestowed fractions of power among these carefully selected and chosen mortals, (an amount like Daniel was reduced to), so that they may also one day join a preconceived X-Continuum. ("The Nega'Jem, Part II")
These power-bestowed mortals would come to be known as omni'X. There were usually two ways an omni'X could grow with their power much faster, other than time - one was to meditate, and another was to fight. Some of these omni'X were mere crewmembers on starships. ("Vengeance", "The Nega'Jem, Part I", "Avalon Battlefield, Part I", "Avalon Battlefield, Part II", "BaKardi Slang", "Power Levels", "Broken Pieces")
During this time, in 2377, in fact at the exact moment Daniel was reduced in his power, a part of space was turned chaotic and then encaved in a growing temporal energy. It was egg-like in shape, and called X-Time.
X-Time was predestined to last at least a year and a half in existence. It was created by the rogue X to house all the omni'X, where they would come to finish their growth. In this place, they would all battle against each other - and in this place is where the X-Continuum was almost created in full. It was said one could only enter X-Time at its creation or right at its end. ("Avalon Battlefield")
The X-Continuum was never actually created before 2383.
- Although, it is perceived that the time in which the rogue X were running around, was when the first X-Continuum was in existence. - More specifically a "first phase" X-Continuum.
During the end of X-Time, Q himself came to retrieve the foolish rogue X and return them to the Q-Continuum. The fate of all the omni'X were that they remained what they were... half mortal, half omnipotent. Though once promised by the Q-Continuum that these types of beings could not exist, it was ruled harmless for omni'X to go on. As for the X-Continuum, it remained a goal that many omni'X still believe in; that one day, such a Continuum would come to existence for them. ("Avalon Battlefield, Part II")
In 2383, a Talarian omni'X named Rein finally descended into omnipotent status; therefore becoming the first X in existence. His ascendance automatically created an the X-Continuum - although, he was the only occupant of it. ("Broken Pieces")