When I had a cat, I would put a cup of water next to me.

You would use "had" because you are referring to a time period that is in the past. But if you used "have" it wouldn't be wrong! If you said "Before I have a cat," it would sound like you are about to say some condition that needs to be met before you have a cat. Like "Before I have a cat, I need to study how to take care of one".

Had* is in the past . Has is current

Hello! The correct word would be "had", because it is the past tense. (Ex. *Before* you had a cat) "Have" is the present tense. (Ex. You have a cat *right now*) Hope it helps.😊

Definitely before I had a cat. It has to be in the past because it happened before the cat happened.