Not unless you exit and come back using AP回复：Pjiang, my son is 4

My understanding from Pjiang's is that, you may not apply for SSN unless you travel outside U.S. and come back using AP.

The reasoning is simple: with 485 pending, your son is still keeping his prior status, either it's F-2 or H-4. By using AP, the status becomes AOS, and you have reason to apply for SSN.

Please, anyone who has real life experience correct me if I am wrong. I am in the same situation.