Make sure your AirPods Max are charged
Put your AirPods Max near your iPhone, iPad, or Mac
Connect the device to Wi-Fi
Connect the device to Bluetooth
Keep your AirPods Max in Bluetooth range
Wait while the update installs automatically
Leave the AirPods Max connected to power if possible
Check the firmware version on your device to confirm the update
If needed, reset and reconnect the AirPods Max, then try again