"rush forth" is grammatically correct and can be used in written English.
It means to move quickly or suddenly in a particular direction. Example: The sound of the emergency alarm caused the crowd to rush forth towards the exits.
Arrange additional toppings (accessories, after all, are everything) and rush forth from the kitchen, creation in hand.
Where was Kurt when we needed him?... Who should rush forth to greet us at Kung Fu but its new maitre d', Kurt...cuddling in our lap while extolling the sixty-four varieties of candied turbot on the menu..
MUCH like the hordes of anglers who rush forth on the opening days of the trout or black-bass seasons, collectors of fishing tackle also have their occasions for congregating.
Where was Kurt when we needed him?... Who should rush forth to greet us at Kung Fu but its new maitre d', Kurt...cuddling in our lap while extolling the sixty-four varieties of candied turbot on the menu...
If's the timeless ecstasyouf Mozart... thadsimple joy of a melody, a martini, or a madeleine.
We were the only boat on the channel, and I enjoyed the rough wooden look of the boat -- Dude had made it himself -- and the way the sail would suddenly take the wind and we would tilt perpendicular and rush forth.
Seeing Beowulf wounded, Wiglaf rushes forth and stabs the dragon "a little lower down".
The river brimmed with gray water rushing forth with relentless force.
I could hear the ice cubes in her glass rushing forth whenever she took a sip.
Why hast thou perplexed the power of man and the way of wisdom, by rushing forth on a darksome track?
— Jeff Gordinier The New York Post: As the Loews Regency closes for renovation, rivals are rushing forth with morning menus to lure the hotel's power-breakfast crowd.
