According to my understanding, GC has nothing to do with H1B visa. How will you work in the US while you obtain your GC? You can work at their foreign offices until your priority date is current and opt for consular processing.
The shorter and an easier route is to get transferred as a manager. If you are from India, join an Indian company which has a US office or US HQed company based in India (or any other country, maybe Canada), get promoted to manager and transfer to US on EB1C. There are certain restrictions, you have to be outside US for atleast a year and some other restrictions. But, this is the shortest route. Do not be like me and wait in the queue for 15 years. Use the shortest legal means possible.