What infrastructure? They don't need too many people living there to manage all these. A landing strip, a pier, couple houses for the maintenance team.
A bungalow and a bar for their parliament.
Good luck putting any of that on a single acre
BTW, USS Harry S. Truman may get retired soon. That would give them plenty of space for anything.
Again, best of luck to them. They had to crowdfund $250,000 for the tiny piece of land, they're a LONG way from being able to do anything ambitious with it. That takes DEEP pockets that they themselves admitted to not having.
It'll be a fun little campsite for a few years though, until it's underwater. Then it's just a heck of a story to tell at the bar.
That sounds like a project for letsbuyanaircraftcarrier.com . No island necessary :)