jump the gun
jump the gun also beat the gun {v. phr.}
1. To start before the starter's gun in a race.
The runners were called back because one of them jumped the gun.
2. {informal}
To start before you should; start before anyone else.
The new students were not supposed to come before noon, but one boy jumped the gun and came to school at eight in the morning.
The students planned to say happy birthday to the principal when the teacher raised her hand, but Sarah jumped the gun and said it when he came into the room.
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Source: A Dictionary of American Idioms