Yes, you can file with the SSN as unknown. The below instructions are from the FinCEN CTR Filing Instructions (page 110 on the pdf and page 98 on the actual document). https://bsaefiling.fincen.treas.gov/docs/XMLUserGuide_FinCENCTR.pdf
*15. TIN (enter number in space provided and check appropriate type below)
Item *15 TIN: Enter the person's U.S. or foreign taxpayer identification number (TIN) without formatting or
punctuation. If the number is unknown, check box 15 “Unknown” and leave Item 15 blank. See General Instruction 12
for information on entering identifying numbers.
Hope this helps!