If there were no other sound waves in existence and you snapped, creating a sound wave, the wave would propagate through the medium (such as air) without interference from other sound waves.
When you snap, the sudden release of energy creates vibrations in the surrounding air molecules. These vibrations travel as compressions and rarefactions, forming a sound wave that spreads outward from the source.
In the absence of other sound waves, the snap's sound wave would propagate freely, expanding in a spherical pattern around the source. As the wave travels, it gradually loses energy due to the spreading of the wavefront.
If you were in an environment where there are no other objects or surfaces for the sound wave to reflect off of, the sound wave would continue to propagate until it dissipates and becomes too weak to be detected.
In this scenario, without other sound waves or objects to interact with, the sound wave from the snap would eventually dissipate into the surrounding medium as its energy spreads out over a larger area, resulting in a decrease in the sound's intensity until it becomes indiscernible.