South Hyrule can not exist in the present. Though, it has existed in the past, and will exist in the future, as long as you are in the present, you can not get to it. That makes the only way to get to it a Time Machine.
South Hyrule is known for its beautiful forests, tropical regions, dangerous deserts, and the fact that is does not exist. That is why nobody has built an Evil Castle there.
This king told everyone about how he had made South Hyrule. Everyone went to go look for it, but they couldn't find it, because at the time, they were in the present. They killed the King for lying, but the legend of South Hyrule lived on.
It was taken by Fake Robotnik and Fake Bowser during the Hyrulian Civil War, and they pretended they were the ones who made it.