There are several synonyms that can be used in place of "set ahead." One option is "advance," which suggests a movement forward in time or space. "Push forward" is another similar phrase, implying progress or acceleration. "Move up" can be used in reference to time, such as moving a meeting or deadline to an earlier date. "Accelerate" or "speed up" are other options that convey a sense of urgency or quickening pace. "Jump ahead" is a more informal phrase that can be used to describe skipping over time or moving forward quickly. Overall, there are many ways to express the idea of "set ahead" with slight variations in connotation.