TLDR:
The word is from a World War II bomb, and its usage in media dates back to the first war films and the media which made word plays out of this fact to describe the films as "block busters".
Google Etymology metrics track common usage of the word by the public, outside of specialist reporting, to start to grow in the 1970s (likely with big blockbusters of the age, such as Jaws).
Long answer:
The 2004 novel Blockbuster: How Hollywood Learned to Stop Worrying and Love the Summer largely attributes this to The Jaws films. This is the book the Wikipedia article references on the subject.
This tallies quite well with Google's etymology metrics of the word, which can be seen here. However, the word itself was used to describe movies, much, much earlier.
There's a fascinating article called Pass the Ammunition: A Short Etymology of 'Blockbuster', written by Sheldon Hall, which describes where the word originated from. I strongly encourage reading it if you're interested in the word's complete origins.
He mentions at one point:
...I was subsequently alerted to an earlier use by Jeffrey Richards’s
book Hollywood’s Ancient Worlds, which quotes a review from the
British Daily Mirror, dated 22 December 1950, of Cecil B. DeMille’s
Samson and Delilah (1949), predicting it, too, to be ‘a box office
block buster’.
So it was certainly in some sense used, to describe films, in the early 1950s.
By the mid 1950s, he discovered Variety articles describing a blockbuster as:
[a film that grosses] $2,000,000 or more in domestic (U.S. and Canada) rentals’ as
well as ‘a relatively expensive picture that can head the program in
all situations’.
In fact, by the mid 1950s, it was in common use in film and media reporting.
Hall then chose to study a number of common conceptions about the origins of the phrase.
One of these is the idea of "block booking" - the system of distribution in which the cinema was obliged to book an entire year’s output from a major studio rather than being free to choose only the particular picture or pictures desired. He noted that in some cases, a highly anticipated film (such as Gone with the Wind was sometimes presented on a singly basis to the films, as opposed to in a unit, and thus corresponds to our understanding of a block buster.
However, he notes that by the time the term block buster entered common parlance, the era of block busting was over - so this explanation doesn't make much sense.
The second conception he studied was the idea of a city block, and the term originating from "block busters" being popular films people literally queued around the block for. Whilst it's conceivable this is how it became a famous word, again the term was already in place before this.
Instead, the first recorded use of the word "blockbuster" was in describing a World War II bomb. This is interesting because the earliest recorded instance he could find of a motion picture discussing Blockbuster was in May 1943, for the film Bombardier. To quote from his article:
The tagline reads: ‘The block-buster of all action-thrill-service
shows!’. (Blockbuster was often hyphenated or written as two
separate words in this period.) As the film’s title indicates, the
choice of metaphor was a deliberate play on the story’s dramatic
content, which concerns a squadron of trainee bombardiers and climaxes
with an aerial assault on Japanese munitions factories.
He goes on to comment:
Not surprisingly, reporters, reviewers and editorial copy-writers for
the trade press also began to exploit the word for its shorthand descriptive
vividness, albeit as a way of indicating commercial potential rather
than a role in the war effort. Thus MGM’s combat film Bataan (1943)
was trumpeted in the company’s house organ The Lion’s Roar as ‘a
block-buster to scatter those wise guys in the industry and the press
who are always telling us that the public won’t support war films.’
Paramount’s No Time for Love (1944) was described by Boxoffice
magazine as a ‘comedy block-buster. Theatre grosses should be blown to
ceiling heights.’ Variety’s review of the musical Brazil (1944)
predicted that it would ‘prove a block-buster at the wickets, a
musical investment for Republic that promises to out-gross any
previous top-bracket film from this company.’
He tracks the decline of the word from around 1944 and noted that it stopped appearing in either advertising or editorial copy. He believed this could be due to the development of the atomic bomb, and the "outdated" nature of the block buster bombs meaning the public were no longer au fait with the term.
The word began to reappear in Variety in 1948, in two separate articles about releases from major studios and from then on was used in reporting until it grew larger and larger in the 1970s (and to present day).