A U.S. passport is good for 10 years, and easily renewable. However, because you are a first-timer, I suggest you apply for your passport now. It sometimes takes longer to get the initial document issued. Don't wait until the last minute. It's not worth the anxiety if you get close to departure and the passport hasn't arrived yet. If you've already applied, good for you. Smart move.
By the way, when it arrives check it out thoroughly to make sure that all the information is correct. Mistakes do happen, and you do not want to be stuck in Ecuador because your name or birth-date on your passport does not match the information on your travel documents.