How to check for presence of 'key' in jq before iterating over the values

You can use the select-expression in jq to do what you intend to achieve, something as,

jq '.result 
  | select(.property_history != null) 
  | .property_history 
  | map(select(.event_name == "Sold"))[0].date'

Technically, to test for the presence of a property, you should use has/1, but in the present context, it would probably be better to use the postfix ? operator, e.g.:

$ jq '.result 
  | .property_history[]?
  | select(.event_name == "Sold") 
  | .date'
"08/30/2004"