Probably when the first defensive structure got attacked and didn't readily surrender.
First Siege of Missolonghi happened on 1822-12-31.
One of the oldest references to the mobile siege tower in ancient China was ironically a written dialogue primarily discussing naval warfare.
A siege engine is a device that is designed to break or circumvent city walls and other fortifications in siege warfare.
Siege of Suemori happened in 1584.
Siege of Oguchi happened in 1569.
Siege of Akizuki happened in 1587.
Siege of Iwatsurugi happened in 1554.
Siege of Serres happened in 1342.
Siege of Purandhar happened in 1665.
Siege of Koriyama happened in 1541.
Siege of Negapatam happened in 1781.
Siege of Paris happened in 1871.