Can zero-knowledge proofs be used to verify a user's identity?

Is it possible to use zero-knowledge proofs to verify a user's identity without the user revealing sensitive data?

Example:

A startup wants to create a social media site with a community of users who are proven to be actual humans. No one person can create multiple accounts.

Conditions:

1. All profiles must be actual humans

2. All humans must prove they are who they say they are by somehow providing their name and SSN

3. The startup must be able to verify that there exists a record containing the name + SSN combo

4. At no point can the startup have knowledge of the user's SSN

I know this is an overly-simplified scenario with clear drawbacks (not everyone can provide a SSN). The focus of this question is the possibility of user verification without revealing sensitive data so I'd appreciate it if we avoid nitpicking irrelevant details.

Followup Questions:

1. Can this approach be decentralized so no institution acts as the central database for verifying SSNs?

2. Is this even desirable? What are some potential harms to the user?

3. Does something like this already exist?