It's a bit of a cop-out to say "It depends on the civ you're playing" but... it really kinda depends on the civ you're playing.
The good military civs pretty much all have reasonably early, powerful unique units. The Huns are a good example: the Battering Ram is vicious, and it's available as soon as you research Bronze working. If you're playing them you want to be picking fights in the ancient era, come hell or high water. Find cities that ain't yours then ram 'em and raze 'em (or puppet 'em if you don't care about your battle strategies having cutesy alliterative descriptions). Rome's at its strongest relative to other civs when its Ballistae and Legions are current, so the Classical era is when you should be aiming to start fighting, and so on.
Absent any special units or whatnot, I usually aim for three timing windows: Classical era as soon as I have Catapults and Composite Bowmen, Medieval era as soon as I've got Trebuchets and Crossbowmen, or the Industrial era as soon as I get Artillery and can outrange enemy cities. I usually avoid picking major fights during the Renaissance if possible, on account of that's where the military unit upgrade paths go bananas and I become fearful and uncertain on account of that. The Renaissance and I just don't get along very well in general.
That's the general idea I follow when aiming for an aggressive game. I usually vacillate between Emperor and Immortal difficulties, and I can vouch for their efficacy on those settings, but I usually avoid Deity and don't play multiplayer so lots of luck if you try to apply any of these ideas there.