The Prophet ﷺ used to deliver the Khutba while standing and then he would sit, then stand again as you do now-a-days.

كَانَ النَّبِيُّ ﷺ يَخْطُبُ قَائِمًا ثُمَّ يَقْعُدُ ثُمَّ يَقُومُ كَمَا تَفْعَلُونَ الآنَ