The First Subbuteo World Cup was held back in 1970.
It was originally organized by Waddingtons, Subbuteo brand owners, every four years at the same time as the football World Cup. 
Only two categories (Seniors and U16) and one player per nation per category were involved. FISTF took over in 1994 in Paris, starting an annual World Cup from 1996, with 6 categories (Open, Women, Veterans, U20, U16, U12) playing individual and national team events. In 2018, FISTF moved from holding the World Cup every year to holding it every two years.

Detailed historic information can be found on the English wikipedia of Subbuteo .