Overall, an interesting underlying societal premise, with only normal levels of suspension of belief necessary to embrace it.
Nevertheless, authors who write military fiction would do well to have it reviewed by someone with military experience before publication to avoid annoying incongruities.
To mention a few here, admirals have barges, not gigs. No admiral, especially higher ranked admirals, captain ships. The respective jobs are incompatible for larger forces, and hard to manage even for the senior Captain who ends up in charge of a smaller force. Even if a Marine became a CO of a ship the size of an LHD, he would likely be at least a Lieutenant Colonel, more probably a Colonel, not a Major. USN LHDs are commanded by Navy Captains, equivalent to Marine Colonels. A Major is equivalent to a Lieutenant Commander in the Navy. Destroyers and attack Subs are typically commanded by Commanders. The Admiral who died would have had a Captain as his Chief of Staff, and probably other Captains and Commanders on his staff. The Major would never have been in command of the task force. One of his seniors would have been. Et cetera.
None of these things are so horrible as to make the story unreadable, but they do serve to jolt the knowledgeable reader out of the flow. And they are easily avoidable.