Air carrier First Officer reported the self-coordination of movement on the ramp due to the lack of Ramp Control at AUS resulted in a hazardous situation between multiple aircraft.

Narrative

Upon arrival into AUS our gate was occupied and Aircraft Y occupying the gate about to push back. We landed Runway 18R and taxied in with Ground Control via C and entered the ramp at C2. We parked on the C2 line to wait for our gate. To our right in the open pad between C2 line and G3 taxiway was Aircraft Z also waiting for their gate and Aircraft A who had pushed off their gate abeam Gate XY. Aircraft Y occupying our Gate XX pushed back and stopped parallel us on the C1 line facing east. Aircraft A abeam Gate XY was ready to depart; and in lieu of waiting for Aircraft Y to start and depart; coordinated a ramp exit with Ground and taxied between our aircraft on C2 and Aircraft Y on C1 with minimal space. Additionally; Ground inquired with Aircraft A if they had room; noticing the multiple aircraft; and once Aircraft A responded that they did; Ground gave them clearance to taxi. Ground; noting the multiple aircraft; could also have encouraged Aircraft A to wait. I was seconds from relaying; 'Aircraft A departing C2 STOP!' on Ground frequency - it was so close to our aircraft. Cause: Lack of Ramp Control at AUS is causal and is a large accident waiting to happen. Each time I have been to AUS the ramp congestion has been a safety concern with aircraft having to coordinate amongst themselves for movement or making dangerous decisions putting other aircraft in jeopardy. AUS needs a Ramp Control as it is a high risk for future safety incidents.