Just got back from my second viewing, found it more enjoyable than the first.
As far as a possible in universe explanation on the Republic/Resistance/First Order situation… It could be that the New Republic, like the Old Republic prior to the Clone Wars felt that they shouldn’t have a standing army and the plan was to have Luke rebuild the Jedi order to once again be the guardians of peace and justice in the galaxy.
So due to past mistakes, the idea of raising an official military for the republic could just be something they see as politically unacceptable and hence we get the Resistance which rises up independently to the fight the First Order after a few initial terrorist type attacks on Republic systems. The Resistance effort would then be secretly supported by the Republic and as stated above it isn’t too hard for the First Order to connect the dots.
The Republic probably initially just didn’t think the First Order to be much of a threat with Vader and the Emperor gone. You’d think that once they destroyed the new Jedi order that should have changed… do we have any idea how long ago that happened and how long Luke has been missing?