This goes back, mostly, to an influential theologian Jonathan Edwards, author of Sinners in the Hands of an Angry God, who believed that contrary to the sacraments of catholics, the way to gain salvation was through a direct experience of God. While this idea is not entirely new and has analogues in other religions, with Christian mystics, and could be generalized for most protestants, this guy was ground zero for the popularization and framing of this idea in America. Protestants generally reject most sacraments or inject a necessity for faith to make them work like in Anabaptism, but the immediacy, the practice of 'revivals' and the radical flair of this kind of protestantism in America goes back to this guy.