There’s a similar expression to the one we just learned, but it uses だす.
先生が話し始めました。 先生が話しだしました。
Sensei ga hanashi hajimemashita. Sensei ga hanashi dashimashita.
My teacher started speaking. My teacher started speaking.
The difference is that だす is used when the action happens abruptly or unexpectedly. This is why ～だす is often paired with the adverb きゅうに (suddenly) and ～始める with やっと (finally).
彼女はやっと話し始めました。 彼女は急に話しだしました。
Kanojo wa yatto hanashi hajiemashita. Kanojo wa kyū ni hanashi dashimashita.
She finally started talking. She suddenly started talking.
Here are some other examples that use だす:
赤ちゃんが急に泣きだしました。 妻が急に怒りだしました。 子供が急に飛びだしました。
Akachan ga kyū ni naki dashmashita. Tsuma ga kyū ni okori dashimashita. Kodomo ga kyū ni tobi dashimashita.
The baby suddenly started crying. My wife got angry all of a sudden. Out of nowhere, the child darted out.