Yes.
Right there will be one time process you need to go through that you won’t need to do again. I don’t have a google speaker but it should have a button to press which will put it in pairing mode. Which is to say, get it to connect to a new device like a phone. Typically you hold down this until a light somewhere on it starts flashing.
Once that’s done, go into the apple options on your phone, which has a wee cog as the app icon.
Once in there look for the Bluetooth option which will have this logo
View attachment 12599
Slide that to on, and it should show you available devices to connect to. The google speaker should have a fairly obvious name, select it to connect.
Once you are connected sound output will go to the speaker automatically which you can deactivate by toggling Bluetooth off.
You won’t have to do the pairing bit again, it should connect automatically if Bluetooth is on. Failing that just go into the Bluetooth menu as above and select the speaker again.