How to find the aquifer in Dwarf Fortress

An aquifer is usually encountered only a few z-levels below the surface, I'd say 6 at most maybe, so if you haven't encountered it by then, it mean it's not there.

There's a possibility you've embarked on a location with two or more different biomes, only one of which holds an aquifer. So your best bet is to just make a lot of short vertical shafts all over your map, until you find it.

Those layers won't ever contain aquifer, so if you're in this layer, you need to dig deeper: - clay (all kinds) - siltstone - mudstone

To see if you're embarked in different biomes, you can look at your surface map and see if tree density changes. Not always, but often one biome will have a very dense forests, while the other won't.

Or you could just start the new embark and check the same place you've embarked before.

In general, once you've reached stone or especially metals, you're past the aquifer depth. The whole point of aquifer is to make those needed materials more difficult to obtain. By the means of fun.