The In Harm's Way series of games revolves around military service. One of the features of this style of play - military roleplay - is the central fact that the PCs come into the game already part of something bigger than themselves, their service. The PCs have access to service assets, work together with other parts of the service, and can mix and match troupe members as needed.
In the game In Harm's Way: Wild Blue, I introduced the Company rules, so that the Players could run their own mercenary company. I developed and expanded on that with OHMAS, where the Association that the players were members of became absolutely central to the game. This concept has worked so well for me that I am bringing it into central focus in StarCluster 3.
I have been running RPGs for 33 years now, and one of the major pains for all of them is how to get the PCs together. Typical PC parties are so disparate, so unfocused, that any sort of reason they work together is a polite fiction. The meeting in a bar is, of course, a classic. So is the chance assemblage of strangers who are all survivors from some disaster. The bad thing about these classic setups is there is no reason for the PCs to stay together once the immediate challenge is done.
Creating the organization first gives the PCs a focus, a reason to work together. It gives a framework for adding others, for troupe play if desired. It gives access to organizational assets. It provides a rationale for continued cooperation. It also - if constructed by the players - gives an indication of what kind of play they are looking for from the GM.
Maybe the organization is a news agency. Maybe it's a government funded scientific research company. Maybe it's a courier service, or an espionage agency, or a TriVox entertainment provider, or a licensed mercenary company, or a bioroid design bureau. Whatever you would like to create should be doable.
And of course, should you prefer those strangers to meet in a bar, that's doable too.