The Prophet (p.b.u.h) used to deliver the Khutba while standing and then he would sit, then stand again as you do now-a-days.
Sahih al-Bukhari Book 11, Hadith 44
← Previous Hadith My father said , "I heard the Prophet (ﷺ) delivering the Khutba on the pulpit and he said, 'Whoever comes for the Jumua prayer should take a bath (before coming).' "

Sahih al-Bukhari Book 11, Hadith 43 Next Hadith → One day the Prophet (ﷺ) sat on the pulpit and we sat around him.

Sahih al-Bukhari Book 11, Hadith 45