I lost my AirPods and they are offline and I don’t know the serial number

no apple device can be tracked by serial number

airpods do not have gps so they don't really know their own location

airpods only means of commication is bluetooth bluetooth has a range of about 50 meters

if this How to find your lost AirPods – Apple Support

then I believe your only option is reporting it to the local police and contact your insurance company