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You can use a DC-DC boost converter (1-transistor boost converter).
You can also use a push-pull converter.
I recommend using the push-pull converter, as, when the switches are off, output is zero, whereas in the boost converter when the switch is off, VOUT = VIN. And the output is isolated from the input as well.
The above shown diagram (in post #4) is like a flyback converter.
An RCD snubber should be used across the transformer primary. Another snubber could be used across the MOSFET (to reduce the rate-of-rise). At the secondary, a single diode followed by an LC filter should be used to convert to DC (the inductor may be omitted) - not a bridge rectifier.