Someone else has already covered ballet in Japan. So, I will explain how it got to the United States.
Ballet has its roots in European court dancing, later was developed during the reign of France's Louis XIV, and remained a French and Italian artwork for a while. Russia, via a French connection, got on board early with ballet, and for a long time, ballet was only really practiced greatly in these three places, hence the reason why there were traditionally Italian, French, and Russian methods of ballet training. The rest of Europe followed suit, but trained in one of these three locales.
The English speaking world really got interested in ballet during the 1800s, most especially during Queen Victoria's reign. This would also be the time most of us would recognize as the parent to pres t day ballet. Even so, it would be many many years before an official ballet theater was created.
The United States first got its taste for ballet during the 1700s, also via a French connection. Some colonials, early on, took up dancing from French tutors, then became travelling performers. Occasionally, French ballet dancers would perform in the new country, and a very few talented early Americans left to train in France. As the 1800s wore on, this French exchange increased, and many former dancers opened private schools in random locales.
Organization largely remained unrealized in the United States and other western countries, with France, Italy, and later Russia, being seen as the centers for all things ballet.
While ballet was available in Britain and America for people to study, and did yield some famous dancers, neither place really cemented ballet as part of their culture until the 20th century, when things escalated very quickly. (I will note, that the US was a bit behind Britain, though).
It does not surprise me that ballet is still not really available in some countries, as the epicenter of ballet has always been around France and Italy. Even places that have fine established schools and methods of training now are not as old as one might think.
My guess would be if someone were to bring ballet to your country, it would be via the same method it has arrived in every other country, namely someone would need to train in another country with an established culture and history of ballet, then establish a school for training bin your country.
I do recommend some of the reading being offered to you, but hopefully this gives you an idea.