Educated guesses...

U3 is a voltage regulator.
The tab is ground, the pin closest to the 300R resistor is output voltage and the other is the input
The switch input to the mcu is the pin next to R3, R3 is a pullup
When switch K1 is pushed therefore the indicated MCU Input goes low and things happen.
So. You could grab a handy arduino out of your parts bin, power it from the voltage regulator which is probably 3.3 or 5v or something similarly useful, connect one of it's pins to the MCU input, and
void setup()
{
delay(10000); // wait 10s
pinMode(whateverpinitis, OUTPUT);
digitalWrite(whateverpinitis, LOW);
delay(500); // hold for half a second
digitalWrite(whateverpinitis, HIGH);
pinMode(whateverpinitis, INPUT;
}
void loop()
{
// nothing
}
Or use one of the other bajillion ways to skin that cat, but a ready to roll arduino pro-mini or nano is probably the quickest solution.