How to run multiple opposing factions.

As the title suggests, I am at a bit of a loss right now. I have three factions: two cults, one insurgency (who are also mercs that can help or hinder the party), I want to start working towards showing their intentions slowly while also having them all move around at the same time. My thought is out of the three one will become extremely powerful as the quests tied to them aren't completed one of them gets much weaker and one is destroyed. However having said that I don't know how to run multiple fronts especially all at the same time with the above plan in mind. I'd like some insight such as should the world change more rapidly, should it be subtle should it be like a "Hey you didn't do this quest so here are the direct consequences of it" I want to run urgent quests and timed quests but I do not know how to execute this in a way that is good for my worldbuilding and fun to tell the players stories. Any help is appreciated.