If 555 is still triggering on power-up, increase R6 to around 100k & or increase C3 =10 uF. As to what state 555 is in a turn on depends on race of V rise on trigger comparator ref, Vr, & V on pin 2. With almost any capacitive loading on pin 2 ( 2 cm piezoe = about 15 nF ) output will be high. With large C ( C1 ) on pin 5, the V rise on Vr will be slightly delayed ; output may stay low. Delaying reset release if long enough will preveny pre triggering= low output.

 

I'm not sure if I understand you. So what happens is that due to the capacitive nature of the piezo, the voltage at pin 2 will be low, hence output is high. If the capacitance at pin 5 is large such that the voltage rise is slower than the voltage rise due to the capacitor at pin 6, then this will trigger a reset, so output will become low. Is this right?

I took out R6 and C3 that is connected to pin 4, and replaced my capacitor at pin 5 to a 141uF one. I noticed that output was high but immediately after that it became low. It seems like it is correct. Then I test by removing the piezo from pin 2, but it does not change anything. I'm puzzled by this. Why is it that without the piezo, the output of the 555 will still become high at the beginning?