"New religious movements" started in the 19th century. Charles J. Guiteau, who shot President Garfield, had been a member of the Oneida Community
Alot of people would put some 19th century groups that went on to become lasting and significant religions into the "cult" category in their early iterations (and maybe later on as well), but that gets more controversial.
As far as pop culture depictions that I'm aware of, the main character in Nightmare Alley seems like what we'd consider a cult leader for part of the story, although he is just out to swindle people and does not ever guy into his own message. The book is from 1946 and the (much tamer) movie is from 1947.
Scientology is from the mid '50s and Dianetics was from the early '50s. There are some SF stories from the 50's and early 60s that have cult-like groups in them, at least partially from people skewering Hubbard.
This book, about the Moonies, came out in 1966
As far as the groups that would be important to the growing awareness of cults in the 1970s, The Children of God were around already but I don't know how famous they were. Jim Jones was around but I don't know how much media attention he was getting.