Rastafarianism did not originate in Ethiopia.

It has its origins in the Carribean and North America through an association of Black thinkers that notably included Marcus Garvey.

The association with Ethiopia, more specifically the belief that Emperor Haile Selassie is a messianic figure and the divinely appointed ruler of the world, comes about because of a statement that Marcus Garvey made in 1927 saying that a messiah would appear in Africa to build a new Zion for black people.

I have encountered this question before, so here is a more extensive write up about it