Straight off the bat adverb phrase
Without thinking or waiting from the start.
Though she disguised herself as a boy, I recognized her straight off the bat.
She answered all the questions straight off the bat as if she had known all of them before.
Straight off the bat, I thought of my missing dog when I saw that familiar neck belt.
At once.
At once.
This phrase dates from the first half of the 1900s, and it refers to a baseball being hit by a bat.
To long for something/ to do something
I'm itching to go to a tranquil place of quiet beauty.