They either start by one side believing the other side fired a nuke. (See: Every close call having to do with a communication failure/false detection.)

Or by one side believing that firing a tactical nuke is the only way to accomplish their goal. The battle doctrines of both the United States, and Russia, permit the use of tactical nuclear weapons in conventional military engagements. I wouldn't be surprised if, in a shooting war, some idiot were to actually use a tactical nuclear weapon, believing that it would not escalate into an exchange of strategic nuclear weapons.