Well, If you want to have real mil s-f, you would have to basically go Band of Brothers, where you follow a contingent on peace enforcement mission, that get's pulle out, resupplied end send to the fronts of the first battle of Harvest, for example, followed by the exodus from the outer rim colonies, wich is completely doable or quite literaly go the path of the least resistance and follow the story of UNSS Galatea, one of the last Halcyon class warships in service being prepared to function as museum ship, that is militarised once again ans send to the frontlines.
Problem is that any of these and similar ideas would went full military which seems to be not politically correct enough or becoming a called a rip off of some other successful media, mainly BSG. But seriosuly there is no other way. And for that you need a speciallist consultant on the plan and helping writing the script and creating whole content from the gound up.
It is trivially easy, but neither politically correct nor cheap.