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 Tripoli happened in 1102.
Siege of Doullens happened in 1595.
Siege of Trsat happened in 799.
Siege of Ostend happened in 1604.
Siege of Shkodra happened in 1474.
Siege of Kagoshima happened in 1587.
Siege of Kunduz happened in 2001.
Siege of Pembroke happened in 1648.