Please describe the feature you would like to request.

I would like to be able to programatically set focus on the first tab in an template-referenced exported Material Tab Group instance, much like the focus method on MatListOption#focus. or MatMenu#focusFirstItem

What is the use-case or motivation for this proposal?

It's very "nice to have", but it would make the available API consistent with other Material Components that has focus methods.
Any available focus method is helpful in avoiding document queries. Code feels cleaner without them.