Apple Music on Google Home isn't available in all regions/countries. Apple don't seem to maintain a list of what those countries are unfortunately, but if you're not seeing the option it's likely not yet available in your country.
I hope we were able to answer your question with the info provided by @David_K. If you have additional questions, feel free to respond to this thread and we'd be happy to further assist you.
We haven’t heard back, so I'll be locking this thread if we won't hear from you in 24 hours. Feel free to create a new one if you have more questions or have other concerns in the future.
