If there is no other identity using this SSN, then the likelihood of the fraudulent activity being dectected is low.
This is why SSNs belonging to elderly people, children/teenagers, and the recently deceased are of relatively higher value for a lot of people out there doing identity fraud.
Synthetic identity fraud involves you making a bunch of inquiries with completely fake SSNs and squatting on them for a few years, maybe bringing them out of cold storage every so often to make a few more inquiries to keep them on the credit-building radar before you ultimately qualify for actual lines of credit and do a bust-out. There is no oblivious meatbag being used as a patsy-- the identities are completely fake, which is what makes them synthetic.
Using a completely fake SSN instead of a stolen SSN is what distinguishes "synthetic identity theft" from "synthetic identity fraud".
The identities in both cases are completely fake, but only in the identity theft case is the synthetic identity backstopped by a legitimate SSN that belongs to a real person somewhere. If that real person is a child or "off the grid", then the CRAs have no idea who the real person is and their SSN is ripe for creating a synthetic identity that will probably go undetected for years.