It's not. It's possible to use already with the present, but not in this sentence. Already can go with past, present, future perfect, present perfect, and past perfect.
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Grammar GeekAlready can go with past, present, future perfect, present perfect, and past perfect.Hi, GG.
khoffThat's a typo -- it should be "I had already had dinner..."[Y]Ouch! You're right.
RyanLI believe it will be correct if you change "give" to "given".You need a helper there (auxilliary verb).