If we say "already", we will almost always use a perfect tense.
If we were using past tense, we will use "had" for past perfect.
When Sally came home yesterday, her husband *had already cooked* dinner
If we were talking about the present, we would use present perfect with "have"
I *have already read that book*, so I don't need to read it again.
If we are talking about the future, we will use future perfect.
By the time Bob arrives at work tomorrow, I "will have already arrived* two hours earlier.