Should I wait until I get my SSN before registering my company?
Having a social security number is not required to form a U.S. business or obtain the EIN, however, having one does make obtaining the federal tax id (EIN) a little easier.
The company should be formed with the state before it may apply for the federal tax id, and the states do not require any type of U.S. presence or documentation to register the business. With that in mind, it would likely take more than a week's time to register a new entity, so you could start the application process now, and when you obtain your social security number we can then use it to apply for the EIN.
Most likely, if you are receiving the SSN within the next week, you would have the number ready before the state the registration is complete, so you wouldn't lose any time or create any complications.