I don't know exactly where the movie starts in this scenario, but as for the politics of it all, this should have been the basic set up...
- No evidence or inkling of The First Order when the movie begins. Yes, the Republic is still trying to find its footing, but there's no Empire-like faction out there that anyone knows of.
- Maybe an entire, far-off planet is then destroyed - or there's some other mysterious incident - that alerts Leia to some kind of possible Empire-like resurgence, or maybe even the frightening possibility of a new, Death Star-like weapon. The point is, there's a bit of evidence, it's a mystery, and Leia is the only one who's starting to take the rumors seriously.
- Having "a bad feeling about this" after further evidence mounts, Leia forms a Resistance of sorts to get to the bottom of the mystery / combat whatever it is that's out there.
- Then, in some grand way, The First Order finally makes itself known to the Republic, like a giant, well-oiled terrorists group coming out of the woodwork. This way, we get to discover The First Order in the same way the characters do, and the Republic's/Resistance's questions are the same as the audience's questions. In other words, it's ok to be in the dark because the good guys are as well.
- From there, Snoke makes more sense in the context presented as well. He can be a mystery because NO ONE knows who is or where he came from.
- The kicker would then be Han and Leia actually discovering that their son - who has been missing for years - is a central figure of The First Order, which is FAR more interesting than just hearing them kind of talk about it briefly after the fact.
Overall, I just hate movies like this where the characters already know everything, and a lot of the dialogue is simply expositional / just trying to catch the audience up to speed. Why not have the characters discover all of this stuff as the audience does? It's so much more engaging that way.