From what I've read, the AN
-124 was more of a direct response to the US designing/building the C-5A
in the late 60s. With basically twice the payload capability of the An-22, the Russians needed to move forward with a comparable platform.
If you're into the Antonov cargo airplanes, here's an excellent book to add to your collection:
"Antonov's Heavy Transports: The An-22, An-124/225 and An-70" by Yefim Gordon, Dmitry and Sergy Komissarov.
Lots of details, photos, etc.