In the time of the Crusades where did the Via Dolorosa, the route of Jesus through the city of Jerusalem from his condemnation to his crucifixion, begin?

It began at the Antonia Fortress and continued for around 600 meters (~2,000 feet) to the Church of the Holy Sepulchre.

https://en.wikipedia.org/wiki/Via_Dolorosa

During the time of the Crusades, pilgrims believed the Via Dolorosa-Jesus's final walk through Jerusalem-began at the Antonia Fortress, near today's Lions' Gate. This was thought to be where Pontius Pilate condemned Jesus. From there, the route wound westward through the city to the Church of the Holy Sepulchre, where Jesus was crucified and buried.

Though later research points to a different trial location, the Crusader-era path remains the basis for the route followed today.

https://www.holylandsite.com/via-dolorosa