An adverb is a word that is used to modify or to describe a verb, an adjective, or another adverb. They give us information about how, when, where, or how often something occurs.
In this sentence, early is functioning as an adverb, as it is modifying another adverb (tomorrow). As an adverb, early means near the beginning of a particular time or period. In this case, it means near the beginning of the next day (tomorrow).
Tomorrow is also an adverb in this sentence. It is an adverb of time, thus it emphasizes when an event will occur. In this case, tomorrow modifies the verb starts, emphasizing when the race will start.
These two adverbs together, early tomorrow function as an adverbial phrase of time, stating when the race will happen.
