Immediately upon opening one's mouth; at the very beginning of one's speech — used to indicate what someone says first when they begin speaking.
開口一番、彼は謝罪の言葉を口にした。
Right at the start of his speech, he uttered words of apology.
会議で開口一番に質問を投げかけられて少し驚いた。
I was a bit surprised to be asked a question immediately after opening the meeting.
彼女は開口一番、昨夜の出来事について話し始めた。
She began talking about what happened last night as soon as she opened her mouth.