An air carrier pilot reported after pushback they observed another aircraft being pushed back towards their aircraft. The pilot yelled 'stop' on ramp frequency to avoid the collision.

Narrative

We were given push back clearance to push deep into the alley off of our gate; XX. Our ground crew pushed us back what they considered to be deep enough. Ramp Tower never questioned nor verified that our aircraft had been pushed deep enough for their liking. So; the push crew disconnected us around XY Gate and left under normal circumstances. Ramp Tower cleared a 737 to push in front of us which is where the congestion began. First; the 737 left wing walker was no where near the left wing. From my perspective they were closer to abeam the cockpit than the left wing. As their push crew continued I noticed that they were on a trajectory to get very close to the nose of our aircraft if they continued pushing at a normal pace. A few seconds later I yelled; 'Stop!' over the ramp frequency as I felt they were seconds away from pushing the 737 in our aircraft. The message must have been relayed because the tug driver of the 737 stopped rather quickly. In my estimation the tail-cone of the 737 stopped within 10-20 feet of our nose. I'm convinced without any interdiction on my part the push crew would have continued until there had been a collision. The ramp controller was silent throughout this whole interaction. Her existence seemed to be passive rather than proactive. I was a bit bewildered at the situation because; in my experience; ZZZ Controllers are usually on top of the game rather than sitting in the stands. Frankly; I expected better. I bring this incident to the committee because I believe we need all the risk mitigation we can handle given the start of the year. Simply; a lack of communication is to blame for most of this situation. The ramp controller didn't verbally verify that our aircraft had been pushed back far enough. Perhaps; assumptions were quietly made. The situational awareness of the 737 push crew wing walkers appeared to be degraded and the tug drivers view of our aircraft may have been blocked. The ramp controller's lack of assertive control over the ramp played a big factor. There was no intervention by the controlling authority prior to my radio transmissions. I would suggest a 'push deep' call accompanied by some marking feature such as a gate to push abeam to. Not all crews are familiar with every ramp. Second; the ramp controller's need to be more assertive especially at airports such as ZZZ.