If you want to increase your chances without hacks; generate a new world, copy over or select a new region/island, then look for these parameters - Max Megabeast Caves, Titan number. You'll want to increase the former and decrease the latter. To make caves visible, look for make caves visible near the bottom and set it to yes.
Reasoning being that increasing the megabeast fauna in worldgen will increase odds of dragons surviving worldgen and visiting your fort, while reducing the likelihood of semi megabeast fauna eg. cyclops, titans, etc.. visiting your fort. Do note that if you're using version 40.13 and not version 34.11, greatly increasing megabeast numbers will greatly increase the chance of civilization extinctions within the first few decades. You might need to gen a few worlds and check legends to make sure you have quite a few pairs of breeding dragons still in the world, as well to make sure your own civilization and other civilizations (goblin, elf, human) still exists.
All this is assuming you want to muck around in world gen to optimize chances without hacks.
Alternatively you can use DFHack's "embark anywhere" to embark on a dragon cave as Will_Tuna suggests, to get guaranteed dragons and !!FUN!! from the first year.
And of course... you can COMBINE both options to greatly enhance your likelihood of !!FUN!!