When was the omen invented?

Answer 1

I would say that omens and the interpretation of them has been with us for longer than written history.

Humankind tends to need the reassurance of knowing their gods (be they upper-case single or lower-case plural) care enough about them to watch over them and send omens to warn of up coming events (both the good and the bad).

At an early point man became consciously aware of his surroundings and started noticing that some naturally occurring phenomenon where commonly followed by certain other occurrences. For example, when the evening sky is red at sunset, the following day tends to dawn bright and clear. Hence the "red sky at night - sailor's delight" omen.