What is the safest and fastest solution (method) in this situation?
If you are asking about all or some of the masks as your title suggests, it has happened before.
One such example from 2008 is Qantas Flight 30.
After the accident, numerous passengers said that some oxygen masks did not deploy, whilst others had deteriorated elastic. Consequently, it was reported that one passenger smashed a panel of the ceiling to attempt to gain access to the masks. It was stated that these passengers were deprived of oxygen until the plane was lowered to a breathable altitude.
Best thing to do is to stay clam, and to breathe slowly/normally (deep calm breaths).
Worst case scenario if a person is a smoker and obese, they'll pass out but will regain consciousness when the pilots reach a lower altitude. In a rapid depressurization emergency, the pilots act quickly to descend, it will be a matter of few minutes until the air would have sufficient oxygen again.
Pilots have different mask systems that should be tested routinely.