Air has a "taste", much like water has a taste, but mostly what we taste is the stuff that is not expected, like salt, or sulfur. The non nitrogen-oxygen stuff (for air) and the non-H2O stuff (for water). The "contaminants". We taste those because they could make the water or air be poisonous for us. Oddly, we do not detect (smell/taste) some deadly contaminants like carbon monoxide. Inert gases, sure, that makes sense, but CO is pretty deadly so you would think the body would have developed a way to detect it. I suppose it is too similar to O2 for us to tell the difference.
Taste and smell are closely related so hard to truly talk about them as separate things. I "taste" sulfur in the air, myself. I also smell it, but I can definitely taste it.
Could you make a paste from air? Not very easily. You could "pastify" air by adding paste stuff, but the paste would still be the paste, not the air. You could, I suppose, cool air down enough that it took on a semi-liquid semi-solid "paste", but that would be darn cold stuff or very high pressure stuff. Probably more a slurry than a paste.
It is not really a case of familiarity that causes pure air (or water) to lack a unique taste. It is that we have no detection system to detect its taste, because otherwise it would dominate our tastes and interfere with tasting (smelling) things that matter. Sort of like why we don't feel ourselves moving through space as the earth turns. If we did, it would fill our brain with that sensation.
You can also become habituated to common smells or tastes, and learn to ignore them (like how city dwellers tend to not notice the sour stench of unburned hydrocarbons; "smog"), but that isn't really what happens when it comes to air.