Sorry, I didn't mean to suggest that only explosives can trigger an avalanche, obviously that is not true. Lots of natural and human activities can trigger an avalanche, shouting and even very loud soundwaves are simply not one of them. More here if you're interested: https://utahavalanchecenter.org/avalanche-problem-toolbox
At some point something is so loud it stops being "sound" and starts being "shock" and imparts so much energy it can break things or set things on fire.
If you want to draw a distinction, ~194 dB is probably the place to do it (in Earth atmosphere). That's where the sound pressure oscillates between 0 and 2 atm and any louder would necessarily distort.
Regarding the distortion, the error due to wrongly assumed superposition becomes noticeable before that. At this point, the non-linearity of soundwaves becomes glaringly obvious.
One way is wind loading... snow falling in a storm gets blown around and piles up on a slope that's already loaded. Another type - a wet slab avalanche - triggers when the sun melts snow and causes water to flow between the various layers in the snowpack, causing two layers to slide.
The goal of the bomb is to thump the snow hard enough that if any weak layers of snow exist below a hard slab of solid snow, the slab will crack, slamming air through the weak layer, breaking the support of the rest of the slab and causing a slide.
Naturally occurring avalanches usually need some obvious change of force on the snowpack, or some reason why a weak layer becomes weaker. I'd guess that a sonic boom, or definitely a scream, couldn't do enough in almost any situation to tip the balance.
Then how do they happen naturally?