Obtaining EIN without social security
To obtain an EIN for a sole proprietorship the sole proprietor would need to either have a social security number, or an ITIN.
It is possible to obtain an EIN for a U.S. registered business, such as an LLC or a Corporation. You do not need to be a citizen, have a U.S. address or social security number to register a company in the United States. With all that being said, please be aware of the implications of staying in that country illegally, and consider taking the necessary steps to make your presence here legal.