The memory of Jesus’ triumphal entrance into Jerusalem was celebrated in very ancient days in much the same way that we celebrate it today: "The Sunday that opens the paschal week […] all the people climb up the Mount of Olives […] When the eleventh hour arrives (that is, five o’clock in the afternoon), the Gospel passage that talks about the children who went before the Lord carrying branches and palms is read […] The bishop rises to his feet, and all the people with him.
From there, that is, from the top of the Mountain, we continue on foot; the bishop constantly sings hymns and antiphons; ’Blessed is he who comes in the name of the Lord’. All the children, even those who cannot walk because they are too small and are carried on their parents’ shoulders, have branches in their hands, either palm or olive. In the same way that the Lord was escorted, the bishop is escorted. From the top of the mountain we continue to the city and then, after crossing the city, to the Anastasis." (Etheria, end of 4th century).
Beginning in the 9th century the procession began even farther away: "About a mile away (from the site of the Ascension) is the place where Jesus sat upon the foal of an ass. There is an olive tree there from which every year, after paying the price, one cuts a branch; in this way, one enters Jerusalem in procession on the Day of Palms" (the monk Ephiphanus). Mention has been made of the existence of a 4th century church in memory of Jesus’ meeting with the sisters of Lazarus, Martha and Mary on the Bethany road. (Etheria).