Transformer works on PWM at 50Hz?
If you want to generate 50 Hz power, then PWM at 50 Hz isn't really PWM, it is just a square wave at the intended frequency.

Driving the transformer with a square wave is not optimal.  You can think of the square wave as containing content at 50 Hz and other content at harmonics.  Only the 50 Hz content will contribute to what you ultimately seem to want.  The harmonics will cause extra current in the transformer without any benefit.  This extra current will waste power, heat the transformer, and also drive it closer towards saturation than just a 50 Hz input would.

You can use PWM at many times the desired 50 Hz output to drive the transformer with what it will see as a sine wave.  With PWM in the 10s of kHz or more, the inductance of the transformer will filter the train of pulses to their average.  If you vary the duty cycle according to a sine, this average will be a sine, and the transformer will essentially be driven with a 50 Hz sine wave.

You can use another transformer to step up 60 V to 120 V.  However, each time you run this thru a transformer, you will lose some of the power to heat in the transformer, and the impedance will go up.  How much of that is acceptable is something you have to decide.