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Answer by John Burgess, Former US Foreign Service Officer, with over 40 years of living in Muslim countries and countries with large Muslim majorities
It could be done, but it would be a major technical and financial effort.
First, you'd have to locate your country-to-be outside of everyone else's 200-mile maritime Exclusive Economic Zones (EEZs).
Next, you'd have to build your island. A major difficulty is that all those white areas are in deep -- very deep -- water. The little blue spots -- already claimed -- represent volcanic regions that have land poking out of the surface of the sea.
Finally, you probably want to stay away from the borders of tectonic plates ... they tend to produce earthquakes, volcanoes, and tsunamis.
Without spending a lot of time on it, it looks like there might be an area in the Oman Basin, east of Oman, south of Iran and Pakistan, and west of India that's only 200m (656 ft) deep, and outside everyone's EEZ.
Now, I'm not a civil engineer, but I think it's going to take a whole lot of money to build an island up from 200m beneath the sea. While oil platforms are constructed in deeper water, they're not terribly big. They surely wouldn't support agriculture, energy production, and supply water for much of a population. It could be done, though.
If you're actually going to build from the sea floor up, that's going to take a remarkably large amount of fill, rocks, sand, etc. Not only will you have to procure these materials, you'll need to find a way to ship them and put them in place. You're also going to have to get more serious about the infrastructure if you're going to have even a few hundred citizens in your state. With enough money, though, I'm sure it could be done.
Finally, you're going to have to deal with political problems. The surrounding states might not care to have an independent state suddenly appear among them, especially if that state's politics are unknown. I'm sure your powers of persuasion will ease that worry because, of course, you're not armed or anything.
Oh ... you're not armed. That might make you rather attractive to the pirates operating out of Somalia, who are armed. It might even make you tempting enough for pirates operating out of the area around the Moluccas in SE Asia. You might want to be armed after all...
Perhaps you need a treaty with someone who can offer protection? What you have to offer a protecting state in return is an interesting question.
Hmmm ... this isn't looking good. You're going to need the GDP of several small-to-medium states to pull this off.
Maybe you should think smaller? Perhaps, for only 10 percent of the cost of building an island from scratch, you could buy one from a Caribbean country, or perhaps one of the island states of the South Pacific. You might not get full independence, but you could probably buy yourself statehood within an existing country. You'd have to go along with basic national laws, of course, but you could appoint yourself governor, tweak local regulations as you like, and run things pretty much as you like.
I neglected to address sovereignty!
All you need to do is declare yourself a state and get a bunch of other, already established states to go along with you. If a sufficient number (either lots of them or a few very big ones) agree, then you've made it!
If they don't agree ... quickly work really hard on getting one of the big states -- preferably one with a big army/navy/air force -- to agree with you. Then, sign a treaty, also really quickly. Otherwise, somebody with any size army/navy/air force is going to come by and kick you off your island. If you're lucky, they'll give you a boat.
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