Really shy new puppy?

[Max McCoy]

You don't tell enough for us to rule out "mistreatment" as a second factor. But THE big factor is going to be genetic, not helped by the dam almost certainly having a poor temperament.
In addition, if your guess at the age is correct, the pups are at the end of their "need security" period that usually runs from 13 through 16 weeks old.

The easy period for puppy familiarisation & confidence-building is long-gone. To take full advantage of that priceless period you need to bring a pup home at 7, 8, or 9 weeks old.

I don't believe that you went to the breeder's KENNEL - I think you mean the SPCA or a rescue group. But if they are at their breeder's, never go there again. Tough on the pups, but they should never have been born, and giving that person MONEY for any of them will just encourage him/her to do it again.

However, if it is, as I think, a rescue group situation, your first - and URGENT - step is to ask around (Animal Control, vets, SPCA warrant officers, police) about the operator's record. Some people CLAIM to be operating rescue kennels but are actually unscrupulous con-artists or "collectors".

If the litter is genuinely in rescue, I personally wouldn't go near it - my aim is to have only typical breed-worthy GSDs. But your goals are obviously set much lower.
Firstly, the pup WILL be neutered before you get it - that is what the adoption fee from genuine rescue groups tries to cover.

Secondly, examine your goals VERY intensely. People who adopt a pup because they feel sorry for it almost always end up feeling sorry for themselves.
Accept that your pup will NEVER be your guardian. Indeed, she is very likely to be ultra-dependent on you, a clinging vine that relies on you to protect her - which many people mis-identify as "extreme loyalty".
If that clinging "loyalty" is ALL you need, then go for it. But accept that all progress will be very slow. She will NOT be confident enough for you to join a training club with her at 18-22 weeks old, which is the ideal age to start a new pup on formal training, so that YOU get coached before you make too many mistakes in your voice tones & rhythms, your body language, your consistency & awareness.

Be aware that you should not get another dog - and DEFINITELY not a puppy - while she is alive. A GSD should last 12-to-15 years.

Your twitter page must be huge - I eventually got sick of waiting for it to arrive through my tedious 2-to-5kB/s dial-up connection, so went back to the Question with no idea as to how old you are.

Max McCoy, first pup in 1950; GSD breeder & trainer as of 1968