Is it possible to not have any thoughts or inner voices for any length of time?

Yes, it is certainly possible.

I would recommend meditation. Find a comfortable, quiet spot where you won't be interrupted and try to clear your mind. Take regular medium depth breaths and try to relax - first your body and then your head. This can be done anywhere but I recommend being outside the in countryside at a scenic location.

To achieve longer periods of inner quiet some people use sensory deprivation tanks where you spend time sitting in temperature controlled water in complete darkness and silence.

In extreme cases a doctor can prescribe medication to quieten the brain but that should always be a last resort as every drug has side effects.