Discount Records, a fairly switched-on retailer with three stores in the Bay Area, had in fact advertised the new album in the San Francisco Examiner as early as Sunday June 19:

[Thanks to JP for finding this]

However, the retailer would have had to draft and submit the advert at least a few days before the publication date, and that would have been before the delay caused by the June 16 overdub session.  So they were probably just going by Columbia's scheduled shipping date prior to that last-minute delay. Perhaps they were planning to make the 500-mile round trip to Santa Maria to pick up copies from the pressing plant, thereby getting the record in stock several days ahead of rival dealers who waited for the album to arrive via the conventional distribution channels; see this earlier note.

It is interesting that the advertisement listed all the song titles, as there had not been any official publication of the track-listing up to that point.  However, it looks very much as though they received it over the phone – perhaps from a contact at Columbia – rather than in print. They have the contents of the two discs listed the wrong way round, and they have “The Fourth Time Around”, "Obviously Five Believers" and “Rainy Day Women No. 12 & 35” rather than “4th Time Around”, "Obviously 5 Believers" and “Rainy Day Women #12 & 35” as printed on the record labels and sleeve of the released album.  It's also notable that they use a standard Columbia publicity photo rather than a picture of the album sleeve. So we can conclude with some confidence that they did not have any physical copies of the album in hand.  No doubt plenty of Dylan fans turned up at Discount Records' three stores the next day, but they surely left empty-handed.