The original text does not say `the first [day]` of the unleavened bread. It simply says first. I suspect this is the first month in which the feast of unleavened bread was observed - Nissan.
The actual Passover meal was eaten on Tuesday Nissan 14, 31 AD
The day after the Passover meal was eaten was the first day of the feast of unleavened bread - Wednesday Nissan 15, 31 AD - the day Jesus was crucified.
The preparations were obviously made earlier in the month of Nissan -> you can`t wait till the day of the feast to make accomodations for the feast. -> Jesus spend all of Nissan 15 in courts, on the cross and dead.