It's simple. Air is made of N2, O2, Argon, and small amounts of CO2, H2O, and other stuff. "Air pressure" is created by those molecules individually bouncing off the surfaces of things. INDIVIDUAL MOLECULES doing that.
This means, at the lowest level, air pressure consists of noise. Because the "averaging" is enormous, the DC component is what we call air pressure. Obviously.
But, now, let's talk about the AC component. Without going into a whole lot of mathematics that is impossible to type in ASCII, the answer is
"For an average sized eardrum, the noise due to the molecular nature of air is somewhere around 6 to 8.5 DB SPL white noise." Yeah. Really.
Now detectability of noise goes by how much energy there is in every ERB, an ERB being the cochlear filter bandwidth around any chosen frequency between about 20Hz and 19000Hz (hearing above that is limited to the very entrance to the basilar membrane and the filter bandwith at the entrance). At low frequencies, an ERB is about 40Hz wide, give or take. When 1/4 octave is wider than 40Hz, then it grows more or less by 1/4 octaves.
Using all that established knowledge, we figure out that the atmospheric noise is JUST below the absolute threshold of hearing at the most sensitive point in an undamaged person's ears.
Using other established knowledge, we know that a tone is masked by noise in an ERB when it's about 5.5 dB lower than the noise in the ERB. There are some circumstances that may make this number 8dB.
So, let's make this 10dB (being conservative). Using a very narrow estimate for ERB's (that has to be over conservative), the noise floor in the most sensitive band is at about -20dB SPL. This means that detecting tones below -30dB SPL is, frankly, not going to happen.