Rising edge detector negative pulse emitter - how to prevent firing at power up?
You are asking to disable negative edge pulsing while both input and Vcc power up   without a comparator to disable input or output.  

Therefore it is not possible with only 1 transistor.

Therefore you need a powerup disable timer or DC OK  detector to disable inputs.

As Marcus correctly states this can be solved logically or with more analog parts or a register to indicate State for output enable.

What is missing is the time delay after power up and more analog parts.