It appears that Google Search doesn’t track the Internet Archive (Archive.org) in anything like real-time for the useful content. For instance, see:
site:archive.org staffordshire -cannock -bbc
On this search you have to go to “Last year” to get anything useful from Google Search. With September 2018 being the latest datestamp I can see among those results. This gives the appearance that Google is only indexing Archive.org on a quarterly or bi-monthly basis?
Yet a search for…
site:archive.org + the ‘last week’
… does pick up material from Archive.org, but by the looks of it it’s only the utter rubbish, sex fantasies and spam that Google will want to rapidly exclude or make effectively undiscoverable. My guess is that there’s an ongoing low-level indexing of the new material purely in order to identify the junk, expose it to some user selection to try to sift out anything that’s a false-positive, and that this is then fed in as an ‘exclude’ junk-list for each larger quarterly re-indexing.