How can I get every legal document to operate a business without a social security number?
You are able to register a business in the U.S. without having a social security number, and it is also possible to obtain the EIN (although it takes a little longer, about 10 business days). We have a research article titled 'U.S. Companies for Foreigners' which will guide you through the convenient online process details, as well as help you choose the best state and entity type to register.
As for the contractor's license, you would need to consult directly with the department or agency responsible for issuing that permit for their exact requirements, limitations and restrictions. Generally speaking, if you are conducting the business activity in the U.S. and your business employs you, it is important to ensure you have proper personal documentation, including SSN.