When first launched, Google received some pushback about the smart home speakers not being able to pair to an outside audio source like Amazon Echo. There was not even an AUX-out port so you could not even use an external speaker through a traditional 3.5mm jack. You could, however, use audio with a compatible Google Cast speaker or speaker connected to a Chromecast audio.
We still get no headphone jack with either Google Home, but Bluetooth support is now coming with the Google Home Mini (or Max). You will be able to pair a Google Home or Home Mini with a Bluetooth speaker so you can listen with a better-sounding speaker.Google Home Mini
Google Home devices update in the background, so the feature should already be live. To pair to a Bluetooth speaker, "Open the Google Home app, head to device settings and follow the pairing instructions to make it your default speaker." We didn't see this setting on our Google Home Mini, but you should see it soon.
For those with a Google Home Mini, you’ll finally be able to enjoy your music with a better-sounding Bluetooth speaker while still being able to use voice commands.