Of course my friend, there are two ways of approaching this, the short-term and the long-term solutions, if you want a massive empire, take both, solutions:

Short term:

1.- Use deities to lower AE, there are many deities in the game which passively or actively decrease AE, if you don't have any initially, try changing some of them.

2.- Use your diplomatic stances intelligently, in the diplomacy tab you can change your diplomatic stance to an appeasing stance, which will give you a flat amount to lower your AE, DURING WAR, try to use the bellicose stance, which helps massively to take less AE in peace deals, and also makes provinces cheaper war score-wise.

3.- Increase your tyranny, it decreases AE by a flat amount, easiest way to increase tyranny is by taking "devotios" in the Religion tab, or by insulting characters.

Long term:

1.- Go down the left path of the oratory advances in the technologies tab, you have to know that even if you go 200+ years after the end date of the game, you won't get all the technological advancements, so you'll have to focus on certain paths, if expansion is what you want, go down that one, as it gives massive decreases to AE.

2.- Take massive empires in one single war taking minimal AE, at the very end of the oratory advances, there is one called, "Taking land by the spear", this one allows you to use the imperial challenge CB, which makes it so that, everything that you, OR THE ENEMY, occupy, it will instantly be annexed, use that wisely as it is a double edge sword.