No. In order to have a credit rating you must have credit and you can't have credit without an SSN or ITIN.
You do not need social security to run a soft pull: With a soft pull, you can obtain your customers' full credit report and FICO score using only their name and address. A soft pull does not require their social security number or date of birth.
Providing your Social Insurance Number (S.I.N.) is optional. If you provide your S.I.N., we will cross-reference it with our records to help ensure that we disclose the correct information to you. We will not use it for any other purpose or share it with any third party.
It is possible to check someone's credit without a SSN, but you need other identifiers (like driver's license number or full name + address). And in any case, a freeze would have blocked the pull.
While it's possible to have a credit report and credit score even if you don't have an SSN, providing your full identification information is key to ensuring that the report you receive is accurate and complete.
Your name, home address and date of birth. any current credit agreements you have. whether you're registered on the electoral roll. a top-level view of your financial history.