The novel got rave reviews in some publications, mainly because of the fly-on-the-wall view of the Mafia, a subject that has always fascinated people. Puzo provided a level of detail that hadn't been offered in other crime novels, and people eagerly absorbed it.
Now, this is an opinion: Americans have always been simultaneously repelled by, and fascinated with, secret societies. The Freemasons served the purpose in the early years of the Republic. Then we had the Communist Party USA. The Kennedy assassination totally absorbed the conspiracy theorists for years. The Godfather came along in 1969, just as the Kennedy brouhaha was winding down--its "insider" view of the Honored Society was just what Americans wanted to read about.
One other point: Paramount provided considerable hype for the novel. Paramount gave Puzo an advance on GF in 1967, before he'd written it. Although Paramount showed a considerable amount of diffidence when they finally decided to make the film, they were very excited about Puzo's project, and talked it up plenty before it was finished.