Palm Sunday was initiated because Christians worship on Sunday.   

The day Jesus entered Jerusalem on a colt with the palm branches and Hosannahs coming from the people was Nisan 10 which was a Friday.   Exo 12:1-3

Why Friday?   Because Nisan 10 is the day that the paschal lamb was chosen and Jesus fulfilled all scripture.   

Friday April 20, 31AD: (Nisan 10)
- The paschal lamb was to be taken on the 10th day of the first month - Exodus 12:3
- Jesus` triumphant entrance into Jerusalem - Matthew 21:1-11 , Mark 11:1-11 , Luke 19:28-39 , John 12:12-16

Trimphant Entry Prophesied:

Rejoice greatly, O daughter of Zion; shout, O daughter of Jerusalem: behold, your King comes unto you: he is just, and having salvation; lowly, and riding upon an ass, and upon a colt the foal of an ass. Zec 9:9