If you express your inclination for something to happen soon, you can use alternative phrases instead of "would sooner." You might say that you'd prefer to do something immediately, or you'd like to do it without delay. Other synonyms for "would sooner" include "would rather," which is a more commonly used phrase in modern English, or "prefer to" and "favor," which also convey your desire for something to happen soon. To indicate your eagerness to complete a task, you could say that you're keen to do it or that you'd relish the chance to complete it promptly. Whatever phrase you use, the goal is always to express your preference to get something accomplished quickly and efficiently.