I listened to
A Hard Day's Night last week and noticed a couple things about the title line of "Any Time at All." First Lennon sings the line, and then McCartney sings it, and then Lennon sings it again. Because more than one voice sings this line, there's a sense of the breadth of possibility of "any."
The "all" is sung with a melisma (I think it's E D B in Lennon's part and A F# E in McCartney's). This too gives a sense of the breadth of possibility (note, though, that since "all" is in the construction "at all," it functions adverbially).