Google To Notify Old Sites Not On Mobile-First Indexing But Maybe Not New Sites

I asked Google's John Mueller in yesterday's Google hangout if Google will be notifying new sites after the July 1st change over if those sites are not ready for mobile-first indexing. The issue is, by default, all new sites on July 1st will be indexed using mobile-first indexing - even in the rare case that site is not really ready for mobile-first indexing.