You can start a sentence with one quotation mark that is the first of a pair of quotation marks, but there must be additional text between the first and second quotation marks.
A sentence can begin with a quotation: "Maybe," she said.
A sentence can also consist of only a quotation: "Don't look down."
A sentence can begin with a Word or phrase in quotation marks that is not a quotation: "Off-label" use of the drug has increased in the past year.
