I've not had a lot of time to play, sadly (I'm beginning to think I shouldn't have signed up, but with any luck I'll find some real playtime before the beta's over), but it took me quite a while before I found another city, and it was only then that I built any military buildings. Indeed, simply discovering the other city gave me some degree of focus as it had military structures. The time it took before I found that city was the most unstructured and lacking in immediacy.
I'd say that as soon as a player sees a rival city with military structures, pretty much anyone's immediate response is to build something of their own; arms races are a very standard human behavioural response for better or worse. Finding that city in your very first game is a different story.