This question is about long-term migration to a hypothetical unoccupied island, so it doesn't look like a good fit in Travel SE. Seems like a mixture of expatriates.stackexchange.com and worldbuilding.stackexchange.com.

Have a read of this for people who have tried this in various ways: en.wikipedia.org/wiki/Micronation

Watch a movie or something my young friend, I suggest "cast away", then you'll change your mind.

Beyond the fact that such an island is unlikely to exist, it would probably promptly be claimed by one country (or several). There are several doctrines (terra nullius, continuity, etc.) that can be used to give that a veneer of respectability. The real question is whether the state claiming sovereignty over “your” island will bother enforcing it (many self-declared “micronations” were allowed to subsist for some time without much interference).

No country or nation is a recognized ‘owner’ of Antarctica but several nations do claim pie-shaped slices of the continent. One thing the treaty did allow for was scientific research. May be there are in the world some islands with same regulations.

No, it is impossible to live on an unoccupied island. Once you step foot on it, it is no longer unoccupied. :-)

Should be a perfect fit for pirates.stackexchange.com.

I have voted against closing because unoccupied islands do exist and are not hypothetical and while many people would not like to live on such an island, tourists visiting them may have the errornous idea that they are outside the law.

@ThorstenS. while unoccupied islands are not hypothetical, the unoccupied island under discussion is indeed hypothetical.

@phoog Is it ? The only condition not met is:"nobody knows about it". Oceania consists of ~7500 islands, only ~2100 are inhabited. So more than two-thirds are uninhabited, many of them have no names and are only visible on sea maps. So neither "invading" aka illegal housing or visiting them is hypothetical and the question of Potter already implies ("What punishment would I get ?") that he is aware of possible problems.

@ThorstenS. yes, it is hypothetical, because it was identified by the statement "suppose I find an island...." Potter has not identified a real island, so the island we are discussing is hypothetical. Furthermore, even if the island were real, its invasion and visiting would be hypothetical, because Potter has done neither yet. See, for example, merriam-webster.com/dictionary/hypothetical, where the second definition is "imagined as an example."

@phoog Of course in my theme everything is hypothetical. But that doesnt mean that before people did not experiment that. Im interested in your thoughts, and i think the theme is topical.

@ThorstenS. If you read beyond the title, the question is about an island that's not merely unoccupied (that's common) but unknown and somehow not part of any country. Olorua is, according to the article you quoted yourself, “in the Eastern Division of Fiji”, i.e. part of a country.

I am downvoting this question because it seems hopelessly confused (being inhabited, the property of somebody or under the sovereignty of a country are three completely different things) and changing all the time.

This has been tried, with those involved attempting to declare a new state. It didn't work -- Tonga claimed the islands, the other countries in the area agreed, Tonga sent troops, and those living there were sent packing.

@cpast Nice, I searched something like this, but was unsuccessful. Could I add your comment of the Minerva Reefs as example to my answer ?

@MeNoTalk: Or maybe Lord of the Flies.

Count of Monte Cristo?

"Suppose I find an island where nobody is there, and nobody knows about it." There is no such island. We have photographs of every square meter of the planet's surface. We know where all the islands are.

@David Richerby Now i understand that. But for example the island, which is uninhabited, people now about island, but nobody goes there, is also good. Are you working in law enforcement agency?

You'll need more guns than (or an agreement with) the country that had already claim to own that island or else they will sentence you under their laws.

@DavidRicherby I doubt that. Here is a wikipedia article on new islands en.wikipedia.org/wiki/List_of_new_islands. Zalzala Koh is about 6 months old. Are all those satellite photos within the last 6 months?

@emory: Satellite surveillance of the planet's surface is performed continuously by several parties. Landsat—with publicly available images—performs a complete coverage cycle every 18 days.

@kundor I guess Potter has at most 18 days before his private is discovered by the hoi polloi.

There are many islands where nobody goes for extended periods of times but are still part of a country and possibly belong to someone. You need to specify whether you are wondering about what would happen if you find unclaimed land, trespass on somebody's land, settle on a remote island without authorization from the country controlling it, claim independence from a country or what. Those are all very different things.

Also note that islands can be harder to watch effectively and evoke all sorts of romantic ideas of freedom and remoteness but you could just as well camp in some private forest (or alternatively in a national park) or declare the independence of your farm. Legally speaking that would not be very different from trying to invade an island that's merely uninhabited.