Above is a record I've never looked up until now - the copyright registration for the Holmes Basic Set at the U.S. Copyright Office, which maintains the records (and is part of the Library of Congress).
The database can be searched on-line here and includes registrations from 1978 to present. Some older titles are included if they were registered later, such as the Basic Set (registered 6/21/78). The "Basis of Claim" is "rev. text, ill. & compilation". This could refer to 2nd edition of the set (Nov 1978), but more likely just refers to the changes over the OD&D set. Each TSR product seems to have only a single record in the database, regardless of how many editions/printings. There's not another one for the Basic Set until the Moldvay Set, which has a listed publication date of 2/16/1981, giving us a date for the start of the end of the Holmes Era (the Holmes Basic Set was still available through TSR's Mail Order Hobby Shop until at least 1986).
The most interesting piece of information in the copyright registration is the publication date of 7/10/77. This is the earliest date I've seen for the set, but doesn't necessarily mean it was available for sale at this time. The earliest advertisement I've seen is in the September 1977 issue of The Dragon (#9). This advertisement describes but doesn't actually show the set itself, just the cover art. IIRC, Dragon magazines were prepared a few months in advance, which could approximate the July 10 date. A big question is whether the set was for sale at Gen Con X in Aug 1977. There is a record of Holmes being at this Gen Con, although it wasn't until the next Aug that he was honored as a special guest for his editorial work. A few 1st print Basic Sets have been spotted with blank bottoms, and one hypothesis advanced on the Acaeum is that these represent early Gen Con releases (They could also simply be some extra copies where TSR ran out of printed box bottoms and substituted blank ones). I asked Tim Kask (organizer of Gen Con X) about this on Dragonsfoot, and he said it was a possibility but he couldn't remember any specifics. The date listed in the copyright record at least supports the possibility the set was available at Gen Con X.