How is a foreign corporation, setting up a US corporation, going to have a social security number for an owner of the corporation, if none of the owners are US

How is a foreign corporation, setting up a US corporation, going to have a social security number for an owner of the corporation, if none of the owners are US citizens? Is this really a requirement of the underwriters, or the IRS? I remember looking at an EIN form once and seeing that it required a SSN in order to get an EIN. But of course, someone whose never lived in the USA would not have an SSN. This would seem to imply that the USA is only open for business to US Citizens. You need an EIN to do anything that might be taxable in america, but you can't get one unless you have an SSN.