Air carrier flight crew flying B757 aircraft reported uncommanded aircraft movement following pushback.

Narrative

During push back the ground crew cleared the flight crew to start engines. Engines were started and the aircraft began rolling forward. It appeared that the tug was connected to the aircraft; pulling it forward. The tug was not visible to the pilots. After a few seconds of rolling forward a push crew member gave hand signals for the pilots to set brakes; shortly thereafter; the tug was observed driving away from the aircraft. The aircraft rolled forward without the pilots knowing the tug was detached. The last audio communication the pilots received from the push crew was cleared to start engines".The ground crew failed to communicate with the pilots to set brakes before disconnecting the tug and headset."