Boys on the Side, with Whoopi Goldberg, Drew Barrymore, and Mary-Louise Parker did this.
In the 1968 movie Skidoo, the only opening credits are seen in a quick flash on a TV that’s shown at the beginning. The closing credits are sung.
I can’t remember whether West Side Story had a title at the beginning, but otherwise all credits are at the end, written as graffiti on a wall.
Cloverfield.
Paranormal Activity,
