How to store observations that do not need a start date?

What @Mark said.

Are you in the business of having to combine several datasources together? If so, you either have a common identifier (which goes into the person_id or the person_source_value of the PERSON table). If you don’t have that, and you need to match patients based on identifiable information (name, address, telephone number, SSN and the like) @Mark is right. It’s called “database linking”, and is usually done outside the OMOP CDM, and often even outside your institution, to protect the anonymity of the data.

I would leave the OBSERVATION table alone for this. It is for clinical observations of a patient, not for identification. I cannot think of any clinical research use case that would need SSNs of patients.