The start date column is NOT NULL, so you do need a date. And the only alternative is the service/encounter date.
If the allergy information is from patient history or patient reported the answer of where to put the data is more nuanced because patient history information can go into either Observation or Condition table. You have to think about how analysis will be done using the database. For example, the OMOP Condition Occurrence table is often used to answer questions like, person took drug X and had reaction Y. Or the other way around person has condition X and is treated with medication Y. To do these analysis requires that the condition and drug exposure start dates reflect the state of the person at the time recorded.
If your allergy data is historical or patient reported you can put it in the Observation table, which is where things get put when you don’t want to loose the information, but are not sure what to do with it, or you can still put it in the Condition Occurrence table, but make sure to set the Condition Type concept to ‘EHR problem list entry’ or ‘Patient Self-Reported Condition’. These Condition Type values should be enough to alert researchers to the fact that the condition start date may not indicate when the Allergy diagnosis was made.
I suggest waiting to see if there are some other opinions. Part of answering these questions is to have your answer corrected.