As the Atlantic Ocean began to open, some 160 million years ago (MYA), the North and South American Plates were forced westward, a tectonic process that continues today. In concert, the Caribbean Plate was shoved between them.
The geology of Cuba, which lies along the southern edge of the North American Plate, is complex. It appears that the largest Caribbean island began to form during the Cretaceous Period, some 100 MYA, as collision and subduction volcanism occurred along the margin of the North American and Caribbean Plates, creating a chain of islands. Since that time, uplift, deposition, erosion, Tertiary volcanism and a prolonged period of submersion (from 35 to 5 MYA) have left behind Cuba's varied topography and geology; rock strata on the island range in age from Precambrian igneous rock (900 million years old) to late Tertiary marine limestone (less than 5 million years old). During the Eocene Period, some 50 MYA, volcanism occurred in southeastern Cuba (then contiguous with Haiti and the Dominican Republic) forming the Sierra Maestra; then, about 40 MYA, a rift valley began to separate these island nations, shoving Cuba westward.
Today we see the culmination of these geologic processes while understanding that tectonic forces continue to mold our planet, Cuba included. Indeed, the rift between Cuba and Haiti continues to widen and the American Plates drift westward, scraping past and interacting with the Caribbean Plate (see Caribbean Subduction Zones and Haiti's Earthquake).