Earliest use to mean importance:
1910, O. Henry, Unprofessional Servant:
- Del had crawled from some Tenth Avenue basement like a lean rat and had bitten his way into the Big Cheese... He had danced his way into fame in sixteen minutes.
- (idiomatic) A very important figure, especially a high-ranking person in an organization.
- He'll be meeting with the big cheese first thing tomorrow, to present his proposal.
an important figure