The answer of the above mentioned question is yes. You can open an LLC in any state of the USA without having a social security number.
You can use our following link to read more about opening an LLC in USA as a Non US resident.
YOU CAN ALSO SEND US AN EMAIL OR CALL FOR ANY INFORMATION. FOR YOUR INFORMATION MOST OF THE USA AGENCIES HAVE CONSIDERED TOP TEN BEST COMPANIES REGISTERING LLCs in USA.