Long ago; a long time ago; already — emphasizing that something happened or was true well before now.
その仕事はとっくに終わっているよ。
That work was finished a long time ago.
彼はとっくに帰宅したと聞いた。
I heard he went home a long time ago.
宿題はとっくに提出したはずだ。
I should have turned in the homework long ago.