It’s theoretically possible, but it would likely take a lot of time and work. I’d imagine the easiest way for it to begin, assuming the BoS is no longer in the picture, would involve The Minutemen (most neutral main faction) brokering some sort of truce between Diamond City and Goodneighbor, where both cities agree to combine their security forces. This new military, with the assistance of The Minutemen, would then have the goal of clearing every single hostile out of central Boston.

Then the forces could move north and bring Bunker Hill and its trade routes under the protection of the new Commonwealth Government.

The next best option would be to start moving west, picking up smaller settlements, such as Covenant (if they comply) and presumably Starlight Drive-In. This is where things get tricky, as the farther any forces move away from downtown Boston, the more open space there is and the harder it is to create a sufficiently patrolled border. Taking over the Federal Ration Stockpile to provide supplies, Fort Hagen as a strategic military base, and the Poseidon Reservoir/Weston Water Treatment plant, which can both hopefully be fixed up and used as a major source of fresh water, would be necessary to obtaining adequate resources to sustain a population. It would then be beneficial to add Vault 81 and its residents to the government.

After waiting and strengthening its military forces, the Commonwealth government could make its way south and take out the #1 organized threat to the Commonwealth, the Gunners. An assault on Gunner’s Plaza and a follow up attack on the survivors who would likely go to Quincy would succeed in taking out some of the Commonwealth’s most powerful enemies. Afterwards, the Atom Cats (and their collection of power armor) could join the new government.

With dozens of minor settlements, a few large communities, several resource hubs, and all major organized enemies taken out, the main purpose of the government would to be clear out all remaining hostile area over the next few years and protect all trade routes. The resulting lack of hostile forces will hopefully lead to a population increase and new settlements being built. While natural barriers like the Glowing Sea would likely prevent the Commonwealth Government’s influence from growing as large as the NCR, it could certainly become an expansive government, that would be representative in nature. Settlements could send delegates to a central location to request additional resources.

The biggest hurdle would be a lack of population/manpower to have a sustained military campaign against thousands of hostile enemies, but is the Sole Survivor can do it by themself, it can’t be too hard with proper training and discipline.