The best option is not to use a 555. E.g. if you use a CD4060 with a high enough RC clock frequency (i.e. take the output from Q7 or higher Qn), the first cycle error (after you take RST low to release it) will be negligible.
Okay, I didn't have CD4060 so I ordered it, I also looked for CMOS version of 555 timer but it was not available in DIP version anywhere on local sites in my area.
In the meantime while the part arrives, I'll try other combinations with the NE555 and post results.
This circuit is a sort of test jig for testing another circuits that I am making, the requirement is 1Hz square wave is needed at different voltage levels (
12v roughly, 4.7v, 2.7v) on the push of the button, I went with 555 timer because it works up to 15v VCC, with zener diodes on the output I can get the 1Hz square wave in the other voltage levels.
But now observing that the first pulse is a problem with 555 timer. I can't try the circuit shown by Ian.M because I don't have CMOS 555.
The CD4060 looks promising, hope it works with 32.768kHz crystal but I have to use two CD4060, first divide by 7 and then divide by 8 to get 1Hz. Hmmn lets see, I'll post soon.