In so much as sound is the mechanical wave produced by an oscillation of pressure, on the infinitesimal scale, there is no silence; at least in the experiential sense.
Consider the theoretical vacuum, an absolute vacuum of complete emptiness. Silence exists here, but the moment we are introduced silence only exists where we are not; where we are introduced, we bring our inherent non-silence, the intrinsic oscillations of the functions of the living body. The absolute vacuum has no content, it has no media to transmit the sound wave caused by the oscillations of life; any sound dies on the boundary of nothingness. Our body, even when contained within the vacuum, remains something, a medium, or at least a collection of media, to transmit the oscillations; our skeletal structure transmits the waves by means of bone conduction.
It may be the amplitude of these bone-conducted waves is damped such that they do not disturb the auditory system sufficiently to generate a neural action potential; nevertheless there will be an infinitesimal disruption to any equilibrium of the system, there will be, on some level, a mechanical impact upon our being. Alternatively it may be that the frequency of the wave is such that the brain choses not to perceive it as a sound; but even at this level the mental differentiation requires cognitive processing, albeit non-conscious, to determine how the wave should be perceived. Analogous with visible and non-visible light, the brain differentiates between audible and non-audible oscillations through the mental construct of hearing. Evolution, or God, or intelligent design set the brain such that low-level oscillations are not perceived as sounds, but these settings are arbitrary and the absence of conscious perception does not constitute silence. The act of not hearing a sound does not negate its existence. The silence we think we experience is a charade, a manifestation of reality foisted upon us by the brain.
Life is intrinsically non-silent and the act of living precludes the experience of silence.