It is possible. My parish does daily masses without any music.
However, I don’t think this practice will be widespread until, and if, there is a strict, rule-set difference between a Low (music-less) Mass and High (with music) Mass like there once was. I think one of the weeds of the “Spirit” of Vatican II is that it forces nearly every mass to have music, to have hymns, to have singing, and there’s really never the sacredly silent type of mass anymore. This is because the “Spirit” of Vatican II presumes everyone wants to sing all the time, in an attempt at “active” participation.
I don’t get why I just can’t participate with my mind. But no, I’m basically not allowed to do that. I have to do something to “actively participate.” The “Spirit” of Vatican II makes one false assumption: the congregation has to “do” something outward to “participate.” I can’t express how wrong that assumption is. First, you don’t have to “show” everyone to “participate.” Second, just because you’re saying something or whatever doesn’t mean you’re actually thinking about it, or its meaning, or why it’s being done. I can’t tell you how many people I see on Sundays looking at their toes while saying the responses. “Full, active, conscious participation” happens firstly in the mind, and only then with the body. Sadly, people seem to overlook the word “conscious” in that phrase and think that just because you “do” something that you’re “participating,” and get offended when someone brings up the possibility that one doesn’t, in fact, have to “do” anything to “participate.”
How does someone with throat cancer who can’t speak “participate?” If I asked that question to an average parishioner, I’d probably get, “Oh! we make a participation exception for that person!”

Yeah, but I thought the only way to “participate” is to babble some words every few minutes at mass. People participate in their thoughts, not in what they “do” at mass.