You don't need especially caravels. Not every faction has access to caravels. You can use caravels, carracks or great carracks (don't know the muslim ships).
You get a message around 1400 (c. turn 160 in vanilla version) that the world is round. A black region appears in the west of the campaign map. You can build a dockyard where you can build carracks etc. which can cross the high seas. (As Spain you can use also caravels which can be build in the second last tier of harbour after the message that the world is round).
Sail to the west. I don't want to say more; it should be exploring, shouldn't it?
Take several ships and bring two or more stacks of your best armies with young generals. Recruit indian auxilliaries a lot. The Aztecs are really tough enemies.
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