When you close the upper right switch you power-on the circuit and instantly trigger the timer. After you can use the push button to trigger the timer, as normally. The trick is to use a capacitor directly connected to the trigger pin. Look at the left side of the circuit: when you power-on the circuit the voltage across the capacitor is 0 V, so it can trigger the 555. After a while the cap is full charged, but we can use the push button for re-trigger another cycle.
