FYI, there are multiple reports on the Android Enterprise Help Community (https://support.google.com/work/android/community?hl=en&sjid=8020794700293409791-EU) as well as reseller partner community of zero-touch enrolment issues at the moment.
If you see the error "Zero-touch isn't available", it's not just you.
Google haven't (that I can see) acknowledged it just yet, but it's been logged so should hopefully be resolved soon.
Confirmed (11am GMT+1) Google are working on it.
Google state it is now resolved (~7pm GMT+1)
These are short-form posts for small updates and quick thoughts. They are automatically published to social channels, and have their own RSS feed, too.