An illustrative example elevator sill assembly includes a sill plate and at least one support arm secured to the sill plate. A mounting bracket is configured to be mounted to an elevator car. The support arm is supported on the mounting bracket to allow the support arm to pivot relative to the mounting bracket. At least one actuator arm has a portion configured to be contacted by a door of the elevator car to cause movement of the actuator arm relative to the mounting bracket as the door moves into an open position. The movement of the actuator arm causes the support arm to pivot relative to the mounting bracket to thereby cause the sill plate to pivot from a stored position to an actuated position.