APAD: At the drop of a hat

At the drop of a hat means to do something instantly or without any hesitation. It describes a person who is ready to act the very moment an opportunity or a challenge arises, with no need for a formal plan or warning.

It often implies acting at the slightest signal, provocation, or opportunity. Common examples include being ready to leave for a trip immediately or getting angry instantly, while synonyms include "in a heartbeat," "instantly," and "promptly". 

It likely comes from the 19th-century practice of dropping a hat to signal the start of a race or a fight (since they didn't have starter pistols).

He’s so spontaneous; he’ll pack a bag and go on a road trip at the drop of a hat.
Back in the day, soldiers had to be ready to march at the drop of a hat.
My boss expects me to change my schedule at the drop of a hat, and it's exhausting.