Can H3CR-A Analog Timers produce a 0.5-second one-shot output when the power is turned ON?

Yes, it can.
Leave the start input ON. Connect terminals 2 and 6 (10 and 6 for AP models). Set the operation mode to mode E (Interval Mode). Set the time unit to seconds (SEC) and set the time range selector to 1.2.

Reference Information:
Fully turn the dial to 0 for a momentary output of 20 to 30 ms.