Finding the answer to this question the conventional way is stumping my Google fu, as many sources describe Guanahatabey and Ciboney as synonymous. I am referring to the hunter-gatherer Guanahatabey, and the Taíno Ciboney.
The Guanahatabey by all accounts were hunter-gatherers. AKA: Mesolithic. They also appear to have spoken a language completely unrelated to the various forms of Arwakian spoken in the rest of the Antilles when the Spanish arrived.
I found a reference online that credits "José Jiménez Santander and Lisandra Jimenez Ortega from Department of Anthropology, Eastern Center for Ecosystems and Biodiversity CITMA (Santiago de Cuba)" with an archeological timeline for Cuba. Sadly, their reference link is dead (and it reads like it was somewhat sub-optimally translated into English.1
It indicates that Cuba has had signs of human habitation since about 3,000 BCE. The first culture they place as ancestral to the Mesolithic (non-farming) Guanahatabey they date at around 1000 BCE. The quasi-Neolithic Ciboney (Sub-Tainos on the website, Occidental (Western) Tainos on the map below) arrived in 601. Fully Neolithic Taino people (Classic Tainos on the map below) arrived in Cuba in 13012.
Taino languages are (interestingly) part of a larger language family that is found all across South America. Its final phase (before Spanish contact obliterated it) appears to have been island-hopping north through the Antilles from its source in South America. So the Spanish found it at its northern frontier when they arrived.
1 - H/T to The Notorious DbB, who found what looks like it might be their paper in the original Spanish (PDF)
2 - The "01"s seem oddly specific. Perhaps its a weird translation of a Spanish term for "after 1300".