How can I connect to my family members AirTag?

"An AirTag can be associated with one Apple ID. If you want to use an AirTag that someone else has used, they need to remove the AirTag from their Apple ID first. If the previous user removed the AirTag from their Apple ID but they were out of Bluetooth range of the AirTag, then you need to reset it before you can use it with your devices."

From How to reset your AirTag - Apple Support

Unless the AirTag is connected to your Apple ID, you cannot.