No - there isn’t another way to pair.
I would keep notes on what steps you see when you click Pair.
Does it ask for a passcode? If so, do you enter 0000 or something else?
Can you unpair other devices and re-pair them. Sometimes if there’s a lot of bluetooth devices or a microwave oven or lots of WiFi right where you are, you could get interference.
You can control for that by shutting off all other transmitters - all bluetooth, all WiFi including the router and access points and trying to pair just that mac and just that device. Then you restart both devices - full power down, wait 15 to 30 seconds and power up and repeat.
At that point, if the Mac can’t pair with anything - seek Apple service. If that device can’t pair and others can, seek vendor support.