No.
The original concept had the first 3 digits identifying a regional office that issued the number.
And no SSN has been issued with any group of digits having all 0’s

Fore more info Wikipedia is good at this kind of stuff.

I read stories from older university alumni from back when SSN served as student IDs where someone who issued gym uniforms or something like that would wow students by telling them where they were born when they’d tell him their SSN.

It wasn’t until the internet that people started to secure their social. It took the internet for it to be a thing.