Varies wildly, for me. I've played peaceful culture games where I never conquered anyone. I've also played Scythia games where I declare war on the first person I meet within 10 turns of meeting them.
The decision points for me are:
1) Do I plan on conquering, or is this going to be a peaceful game? If I'm planning a peaceful game, I might not plan on DoWing anybody ever.
2) Is there a nearby civ I'm going to have to fight anyway? Sometimes I'm so close to an enemy I know I'll run into conflicts eventually. In this case, ancient or classical is probably the time to beat them up.
3) If I'm planning to win a domination victory but nobody is an obvious early-game target, then probably I'll fight my first war in the Industrial era after getting production cities up.