The point of this circuit is to allow rising edges to send a negative pulse to a 555 timer. C1's purpose is to allow rising edges to trigger a positive pulse which in turn connects output to ground.
I ran a time domain simulation from 0 - 1.2 seconds with .001 interval. I sweep R1 from 1k to 100k in 33k increments. The bottom blue line is the signal from the square wave generator. The circuit passes rising edges as negative pulses as I would expect to "out" but at the startup a negative pulse is initially sent out as C1 charges. Is there a circuit that can prevent the initial firing to the timer?