Starting adverbs are provided in this article. The words listed here are commonly found along with the verb starting in sentences. This reference page helps answer the question what are some adverbs that describe or modify the verb STARTING.
actually, automatically, barely, constantly
continually, daily, definitely, early
finally, generally, gradually, immediately
possibly, probably, really, seriously
shortly, simply, slowly, suddenly
typically, usually, violently
Hope this word list had the starting adverb you were looking for. In addition to adverbs used with starting, other example verb adverb pairings can be found on this site.
You can help by adding more adverbs in the comments. Thanks.