To begin with, "had a jump on," "led the pack," and "got a headway" are some of the synonyms for the expression "had a head start". In addition, synonyms like "took an early lead," "got a running start," and "established an advantage" can be used to replace the term "had a head start". "Started off on the right foot," "mounted the horse first," and "began with an advantage" are other alternatives. The word "primed" can also be used in place of "had a head start" in the context of being prepared for an event. These synonyms can help convey a similar meaning, with subtle variations in tone that can enhance the impact of the sentence.