Was the first SSN to be assigned in the US just 000-00-0001?

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.
- I went to state college in the 90s and they posted test scores with SSNs. That is when I noticed that most of the students had one of two three digit prefixes. Thought it was based on when they were issued, looked up how SSNs worked and found out about the location pattern.
  
  This was before the credit industry hijacked the number and started treating it as a secret code, despite SSNs not being intended for anything other than Social Security.
- When I went to college early 2000's, my SSN was printed directly on my student ID card. It was the unique ID that the university used for each student. Then like a year or two later, they required all the students to get new IDs without the SSN printed on them.
- It wasn’t until the internet that people started to secure their social. It took the internet for it to be a thing.

No, originally the first three digits designated where you lived when you requested your SSN. The middle two were also not sequential. The final four digits were the only purely sequential ones.

https://en.m.wikipedia.org/wiki/Social_Security_number

Naught naught naught. Naught naught. Naught naught naught...... Two. Damn Roosevelt

Cause of parents' death: got in my way-Mr.Burns
Eight six seven five three oh nine. DAMN YOU TOMMY TUTONE!
- Fun fact: whenever I'm in a 7-Eleven, I use whatever area code is for that area and then Jenny's number, and it always brings up an account for their rewards program and saves me some money. Thanks, Jenny!
- .......it's not even enough numbers! You gotta use a REAL social security number, like 000-00-0001.
  
  Oh wait. We established that never existed. Ok. 000-00-0002.
  
  Nailed it!

reported for doxing, uhhh, someone's SSN... maybe...

I don't trust the fact that cum wants his location to be a secret. The location of cum should always be well established.
- The call(er) was coming from inside the house?

The first SSN was number 571, and is now a museum.

Lol wrong SSN, but I think you knew that

No, the first XXX and second XX are location and date identifiers. The last XXXX is your actual number.

That's why giving out the last 4 digits isn't safe. It's trivial to derive the first 5 with public records and a lookup table.