H1B time does not "count" toward a green card. You employer must sponsor you for lawful permanent residency (a Green card) separately in most cases. This often includes a process called labor certification. Depending on the minimum requirements for the position and your country of origin, this process can take many years in some cases. The recommended strategy will depend on your specific facts.
Both you and your employer should contact an experienced immigration lawyer to discuss the process in more detail.