I have a cup of coffee every morning to wake myself up.
I don't usually feel awake in the morning until I've had a cup of coffee.
この場合、次のように言えますよ。
ーI have a cup of coffee every morning to wake myself up.
「目覚めるために毎朝コーヒーを飲む」=「毎朝コーヒーを飲んで目覚める」
ーI don't usually feel awake in the morning until I've had a cup of coffee.
「毎朝コーヒーを飲むまで目覚めた感じがしない」=「毎朝コーヒーで目覚める」
ご参考まで!