I don't propose taking a city, waiting for recuperation, and then attacking an opponent. I propose taking a city, then soon taking another, then another, then another. Basically moving along an exponential growth curve. If you get lucky and no one attacks you during that period, you stand a very good chance of winning. Even if someone does attack you, the rapid regen from all your cities gives you a fighting chance. This strategy works especially well if you discover a lot of cities in your region during the early game.

The problem with attacking an enemy is that it's easy to get into a war of attrition where you both fall behind other players.