Lacking a transition at the 50 percent mark...
Therefore we must start where there is a transition, and construct a time-dependent feature of some kind.
Time-dependent components include coils and capacitors. In other words, analog constructs.
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You mentioned a frequency doubler. Not a bad idea.
This simulation shows what you'll get:
The incoming transitions determine the shape of the output. The output is not at a 50 percent duty cycle.
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Hold the phone, however. Your idea was to get 50 percent duty cycle pulses, at 1/2 the frequency, from a flip flop.
In that case the frequency doubler does provide 50 percent duty cycle output: