How to match the first occurrence of a pattern (or character) except for lines where that pattern is at the beginning of the line?

I have the following example lines:

!foobar foo bar ! foo               ---> NO MATCH
foo bar foo bar !   foo             ---> Should match !
foo bar foo bar ! ! fooo bar !      ---> Should ONLY match the first ! 
! ! foo bar                         ---> NO MATCH
!foo bar foo bar ! ! fooo bar !     ---> NO MATCH

and I would like to find a regex expression that would match only the first occurrence of the character "!" except where the lines if the character is at the beginning of the line. I have tried to no avail using many different combinations (maybe not properly) of negative lookback like ^(?!\!)\!.

I'm planning to use this regex expression as an input for a command that needs forcefully a regex expression, hence I can't use other methods.