First Officer reported problems communicating with ground crew during a pushback.

Narrative

We were pushing back and the Ground Crew was using a non tow-bar type tug. It's difficult to see the tug from the cockpit. We were cleared to start engines and we started both. We were not aligned with the taxi line when the Pushback Crew paused movement. We only heard static from the Ground Crew over the intercom. The Captain never stated; 'parking brake set.' Again; we were not aligned with the taxi line so as we began rolling forward; it looked like we were being pulled forward. Again; this type of tug is not very visible; however I looked right and saw the tug was backing away and I immediately notified the CA (Captain); who applied brakes immediately and stopped the aircraft. We still barely managed to communicate with the Ground Coordinator because of radio static but he did remove the steering bypass pin and we continued with operations.The Ground Crew needs to verify that their headsets are working properly. Not being able to hear them very well with all the static is partially responsible for the breakdown In communication. I also have an expectation that the tug driver will line the aircraft up on the taxi line; which did not happen here and so we didn't immediately notice that the aircraft was rolling forward on its own.