United Earth has hacked out a state for itself. The Solar System is theirs, so is Alpha Centauri, maybe Bernards and Wolf 359, the latter two dead outpost systems while Humanity is working their butts off terraforming every rock it can (explains why Alpha C might not had been 'claimed' beforehand).
Andor and Vulcan are still going at it, while Tellar is pursuing a neutrality status. Earth has fought a few 'wars' with marauders/junk species (alluding to the Kzin wars in TAS), and has had to look out for itself more and more as Vulcan focuses on Andor. Thus how there's a UESN, UESPA, 'Starfleet', with traditions and inertia. Not the neutered weird assemblage seen in Canon where United Earth is a mere 30ish years old and Starfleet is, as well. Right as the Vulcans landed, the United Nations got together and reformed in twenty years, rebuilt, boom. United (Nations?) of Earth by 2083, 2090. Orion freebooters/privateers are the most major concern now, sniping at UE convoys and trade (maybe the UE is exporting antimatter and minerals from their red-star systems?).
The crisis is that Andor, which Earth barely knows, is in a cold war with Vulcan - up to monthly 'incidents'. The Enterprise? (Do we have to call it Enterprise? I mean, I guess, maybe the show should had been titled something else) is launched as the first Warp-5 'do-it-all Cruiser', as a testbed for a new doctrine in the UESN. I would have it be a sexy Daedalus or something akin to it, not the Akiraprise we got. It's a risky investment: before, ships were specialized, so you had monitors, escorts, 'destroyers', transports, diplomatic ships, cargo ships, scientific surveyors, but the Enterprise will combine most of those roles. It's also a deterrent against the warlike Andorians, as it's the best we got.
So the underlaying conflict is how Earth manages the local political crisis. Andor and Vulcan will be shooting at each other but neither has the stomach for a full blown war, and Earth will come along with the Enterprise and Archer and smooth things out when they can, coming from a more detached viewpoint. This may last two, three seasons, sprinkled in with the UESN smacking down pirates, rogue colonies, exploring, finding a lot of wrecks from the WW3-2090 era where nations and people sent ships which way, and developing a tie with Tellar, maybe nudging them on some issues and likewise. I'm fine with the Vulcan subplot that they've 'lost their way' and Archer and T'pol can help with that, and the like.
Season 3 is when the Romulans start to come into play. (maybe the show starts in 2154 than 2151?) They're unknown, their ships are efficient and sleek, they have the advantage of surprise. Start out with a 'destroyed colony' arc, maybe even a nice little Proto-Federation experiment colony wiped out on the far frontier. Here, we can be a bit creative, especially if space in the future will be 'claimed' by Romulans and not regained, so species can come and go, since 'canonically' they'll be under the Romulan Wing or flee off to new space or become minor members later. They're also good at subterfuge and may try to reignite tensions, being basically Vulcans, they infiltrate and do rogue actions against everybody and the hot peace turns back into a cold war between everyone until Archer and Co. come to the conclusion that 'Vulcans have become double agents to some power who promises to undo what Archer and Co have done)', and it goes from there. (They don't have to be correct, remember).
The war...I don't know how you'll handle the war. DS9 will be fresh, and honestly, a war story by itself is just a report. Earth could lead Andor and Tellar and Vulcan, or might be alone and be 'targeted' by the RSE for its interloping. Andor and Tellar might be subverted and barely offer any help. Stuff like that. But if the war has to be shown, it has to focus more on a conflicted T'pol, because there's not going to be a lot of drama coming from Archer. (What, will Merryweather start a colonial/core divide as the 'colonies' take the brunt of it? Meh).
But yea. Fanficing over.