Non-resident American starting business in US
Yes, you would be able to incorporate a business (either an LLC or a 'C' Corporation) in the United States without having a U.S. business address.
Keep in mind, while you can use your home address in India as the business address, you will need to have a registered agent address in the state where the business is located. We offer this service available on our entity formation applications.
If you are unsure what state to incorporate in, I would suggest you consider the possibility of registering in Wyoming or Delaware, as they are commonly referred to as the 'corporate heavens'.