There is no way to get the timestamp of the created event via the JSON API atm. This limitation also applies to parts of the gRPC API see Contract creation time.
A field that you set to the result of getTime on creation seems very sensible. Keep in mind though that you have to trust the signatories of a contract to actually go through your choice instead of creating the contract directly. If they create it directly they can set the time to whatever they want.