When it comes to the phrase "marches the cannon's mouth," there are several synonyms that can be used to describe the action. Some of these synonyms include "advances towards the cannon," "moves inexorably towards the weapon," or "approaches the artillery piece." Other potential synonyms might include "presses on towards the gun," "closes in on the firepower," or "moves resolutely towards the cannon's position." Depending on the context in which the phrase is being used, any of these synonyms could be appropriate and effective choices for conveying the sense of determination and bravery that is required to approach a deadly weapon like a cannon.