Close its mouth at the speed of light?
Close its mouth at the speed of sound?
Close its mouth faster than the speed of light?
Also… wouldn’t it be heavier than the galaxy itself? So it would create its own gravitational pull that’s like extremely strong?
The speed of sound is the velocity a force can propagate in a medium, so yes even assuming such a mega structure is theoretically possible (it’s not) it would close its mouth at the speed of sound.
If you want a galaxy-doom monster, either pick a super massive black hole, a super massime white hole, a super massive black hole coming out of a bigger white hole, or a super massive quasar pulsating high energy X-ray bursts with enough power to kill all life of an entire galaxy