While the group can be new, one with a history creates depth. This should include the formation story of how, why and where the group originated, and what actions they’ve attempted to do, why, and the result, both for themselves and those impacted by their existence and efforts.
A group’s location will influence their origins. We can use any regional conflicts to inspire their rise. If two sovereign powers are at war, for example, we should know what each wants, why, and the tactics used to pursue it. Do they force people to serve in the military? Do they commit war crimes? Are they harming people and livelihoods? Is injustice being forced on the population? Are riches (like access to a mine) being withheld by one power to the detriment of the other? Any of these and others can inspire opposition that leads multiple individuals to ban together and form an organization.
Another option is a weak king who lets forces overrun his kingdom, or an evil warlord threatening destruction, or a supernatural phenomenon that must be contained. These are events that thrust people into action, and when they realize others want to take the same actions, the group arises. War might trigger groups’ creation in other ways; for example, if it ends, leaving something the group considers unfinished business. For example, maybe the “evil” army is defeated, but many groups that comprised it are still extant. This group will go on a search and destroy mission, the first of many. Others might admire this and join the group.
The group may arise from a shared philosophy about what is right and wrong in the world, whether that’s inspired by specific events or not. Each individual will largely agree with the group’s outlook. Such a group may form in peaceful times, where social injustice is in their sights to correct. The group may exist informally before an event triggers them into becoming a more serious organization.
No history is complete without attempts, successful or not, to achieve the group’s goals. Create a half dozen attempts with a mixture of failure and success. Have they fought in battles with others? Just on their own? What famous incidents are attributed to them or foiled by them? Both failure and success should result in the death of members, only a few of whom might be noteworthy. Others outside the group will also have died, including members and leaders of opposing groups, warriors, wizards, and civilians. The latter may be inspired to join this group’s enemies. All will have left a mark on someone, somewhere. Lives might also be saved and cause similar recruitment or supporters.
Some actions may only partially get their ultimate goal, which allows us to grant some success without eliminating the need for their continued existence (if that goal makes them disband). For example, an organization dedicated to keeping powerful magic items out of the wrong hands might perpetually be recovering and storing them. If there’s a wizard cabal that keeps causing trouble, this can cause multiple events. If we want the group gone, killing them in one way, but a more peaceful end means their goal might’ve been realized, but sometimes a new group arises from the ashes of the old.