As others have said, this seems a bit much to hope for. However, the theory at least is clear: If you can reduce R0 to less than 1, it means that on average each infected person passes it on to less than 1 other person. Thus, if you can sustain that rate, the prevalence of the disease gets steadily less and less. Assuming the virus doesn’t remain indefinitely in the environment, it will eventually totally die out.
So the thinking is that if everyone wears masks, then you can cut R0 down well below 1. This would have approximately the same effect as quarantining everyone. And four weeks of that should be time enough for everyone who is currently infected to get over being contagious, and the virus to die out of the environment. So that should be long enough to eliminate the virus.
So goes the theory.
ETA: A counter-example would be tetanus (a bacteria). It remains in the environment indefinitely (residing on rusty nails of legend, but actually on dirty surfaces everywhere). Eliminating it entirely from the human population all at one time does nothing to eliminate the disease.