There are plenty of court cases forcing people to divulge their SSN.
Only six people were forced by federal courts to get an SSN. They were all receiving welfare.
Bowen v Roy 476 US 693 — the only Supreme Court case, concerns SSN for a child
Callahan v Woods 479 FSupp 621
Callahan v Woods 736 F2d 1269
Callahan v Woods reversed 658 F2d 679
Chambers v Klein 419 FSupp 569
Doe v Sharp & Califano 491 FSupp 346
Green v Philbrook 427 FSupp 834 reversed
Green v Philbrook 576 F2d 440
Greidinger v Davis 988 F2d 1344
McElrath v Califano 615 F2d 434
Stevens v Berger 428 FSupp 896
third Callahan case 736 F2d 1269 — SSN for children