There are lots of power-on reset generator ICs available. If you don't have one available, but you do have a microcontroller, you can just use that instead!
This is an example firmware for the ATtiny84 microcontroller that generates a 500 ms reset pulse on PA0 when powered on.
If you connect a pushbutton to PA1 that connects to ground when pressed, a manual reset signal will be asserted on PA0 when the button is pressed.
No doubt you could adapt this firmware for other ATtiny variants.
Run the command
make
to compile the code, and
make program
to load the program onto the chip using avrdude. You might need to edit the Makefile depending on which programmer you have.