A crest and a trough both cause the eardrum to move away from its normal, undisturbed, resting position. Hence, the crest and the trough both embody a loud sound. When there is no sound, the ear drum is still; it is resting in a central position. When sound waves strike the eardrum, it moves the eardrum inward (crest) and outward (trough). The ear converts the inward motion and the outward motion into electrical impulses, which are sent to the brain.
The loudness of the sound depends on how far the eardrum is moved/displaced from its resting central position. Hence, a really tall crest would be associated with a loud sound, but a really deep trough would also be associated with a loud sound. Zero sound would be embodied by a flat line that does not disturb the eardrum at all and doesn't move the eardrum away from its normal, central, resting position.
We can also look at this mathematically. The loudness or volume that we hear depends on the intensity of the wave. Intensity is acquired by squaring the amplitude/maximum displacement. Hence, when we take the square of a negative number, the resulting intensity value becomes positive.
Most sound waves vibrate the eardrum at least ~100 times per second, which is extremely fast. We can't distinguish a single crest from a single trough, and a lot of averaging occurs in the process of hearing. In music, the tones we hear do not change at this same frequency; they change much more slowly than 100 times every second. Hence, it's more useful to talk more about the amplitude of these prolonged waves rather than pointing to a single crest or a single trough, which we can't distinguish anyway.
Sound waves are actually longitudinal. That is, they form rarefactions and compressions in the air, not crests and troughs.
Loudness is subjective and roughly follows the log of the relative sound intensity.
The anatomy of the ear is complex, and the electrical signals are generated by the movement of hair cells in the cochlea. Some hair cells respond to higher frequencies, and others respond to lower frequencies, etc.
Whether the crest moves the eardrum inward or outward is totally arbitrary and depends on the perspective and coordinate system we're using to measure the eardrum's displacement.