According to new official Star Wars content, the First Order was primarily born from within the New Republic. While pieces of the group’s origin story are revealed through Disney’s sequel film trilogy, much about the First Order went unmentioned on screen. Like most events between Return of the Jedi and The Force Awakens, the First Order’s rise has been most directly addressed in books and other Star Wars side content.
In the wake of the Rebellion’s successful assault on the Death Star II, a good portion of the remaining Imperial military fed to the galaxy’s Unknown Regions. There, united with Palpatine’s regime's supporters, they began to rebuild and restructure into the feared First Order. Of course, it stands to reason that not every Imperial sympathizer would have fallen back to the far reaches of space. For decades, the Empire ruled the Core and much of the Outer Rim, meaning that it would have been impossible to identify and expunge every Imperial presence during the New Republic's rise.
New material from The Star Wars Book, discussed on the official Star Wars website, confirms that the First Order had more than mere supporters in the New Republic. The group’s strength was built up directly from within the government itself. During the early days of the New Republic’s rule, representatives working on behalf of the old Empire pushed for more centralized power in the new government, scaring some systems away for fear of losing their independence. You can read the excerpt from starwars.com below.
“While we know that the military might of the First Order was built up in the Unknown Regions by the escaping Imperial leadership in the decades after the Battle of Jakku, the First Order also had its start inside the New Republic. Agents of the First Order helped push for a stronger centralized role of the New Republic government, which in turn caused a political stalemate, forcing systems that fear losing control of their autonomy to break away from the New Republic — in a coalition called the First Order.”
This clarification helps explain why the First Order was able to gain so much power and notoriety without intervention from the New Republic. With their Imperial connections and true military might hidden in the Unknown Regions, the group would have been passively accepted as an equally legitimate government, just as systems like Mandalore existed outside the Republic in the days before the Empire. That perception of legitimacy would have been vital for the First Order to rise to power, so it makes sense why internal agents sowing discord would have been essential in the early days after Return of the Jedi.
It also makes sense that many systems would be hesitant to join the New Republic after the Empire’s fall. While Palpatine’s rule was tyrannical, many in the galaxy blamed the Republic and the Jedi for the destruction of the Clone Wars, sowing a general sense of public disillusionment that fed into Palpatine’s attempts at rewriting history. By the time the First Order’s true nature was revealed, it was too late.
Source: starwars.com