I think that some ad agency devised "Kodak moment" as a knowing rip-off of (or should I say "a heartfelt homage to"?) Henri Cartier-Bresson's famous notion of the decisive moment. Cartier-Bresson's idea seems to be in line with what you have in mind about recording a meaningful event in a photograph. Here is a brief discussion from his Wikipedia page of "the decisive moment":
In 1952, Cartier-Bresson published his book Images à la sauvette, whose English-language edition was titled The Decisive Moment. It included a portfolio of 126 of his photos from the East and the West. The book's cover was drawn by Henri Matisse. For his 4,500-word philosophical preface, Cartier-Bresson took his keynote text from the 17th century Cardinal de Retz, "Il n'y a rien dans ce monde qui n'ait un moment decisif" ("There is nothing in this world that does not have a decisive moment"). Cartier-Bresson applied this to his photographic style. He said: "Photographier: c'est dans un même instant et en une fraction de seconde reconnaître un fait et l'organisation rigoureuse de formes perçues visuellement qui expriment et signifient ce fait" ("To me, photography is the simultaneous recognition, in a fraction of a second, of the significance of an event as well as of a precise organization of forms which give that event its proper expression.").
I think Kodak began using the term "Kodak moment" some time in the late 1960s or early 1970s. "Decisive moment" may sound a bit hoity-toity for everyday photography, but setting aside Cartier-Bresson's uncanny skill at capturing people and other things in motion, it can be understood as asserting that even seemingly mundane scenes may have a crucial instant of revelation where a photograph can capture something elusive in a lasting and perhaps profound way.