Who broke the silence of night in the story "The Sniper"?

No specific person broke the silence in the story "The Sniper."  The opening paragraph describes the evening turning into night and bringing darkness with it.  The story takes place in Dublin, and specifically it is in or happening around the "Four Courts."  The text says that there is the sound of heavy guns.  My guess is that this is referring to mortars or artillery fire of some kind.  The noise is likely fairly continuous, but the story does specifically say that silence was broken. 

Here and there through the city, machine guns and rifles broke the silence of the night, spasmodically, like dogs barking on lone farms.

The author is making a distinction between the heavy guns and the small arms fire of machine guns and rifles.  The heavy guns are essentially background noise and must be present so much that they are essentially the same thing as silence.  The machine guns and rifles are able to break the silence, because their noise is distinctly different and likely not as rhythmic as artillery fire.  

If your question wants to know which specifically named person in the story fires first, then it is the enemy sniper.  He shoots at the protagonist sniper, because a lit cigarette identifies his location.