I am missing the single word in a common phrase that starts with "In a..." and ends with "...minute" that means 'without hesitation.'
A phrase containing a single word in that blank is in a hot minute, but there is some confusion over whether that phrase means "in a short time" or its opposite. There is considerable discussion at the ELU question Since when has “a hot minute” meant a long time?.
A more common phrase containing a compound proper noun in that blank is in a New York minute. Merriam-Webster defines "New York minute" as a noun meaning instant or flash.