"Before you could say Jack Robinson" is a commonly used phrase that typically means before you can even finish saying the phrase itself, something has already happened. However, if you're looking for synonyms to mix up your language, you could try phrases like "in the blink of an eye," "in a flash," or "before you know it." Alternatively, you could opt for the slightly longer but still fitting phrase "as quick as lightning" or the equally succinct "in an instant." Whether you're writing a story or just trying to diversify your vernacular, these phrases can help to add some variety to your statements.