If you mean written evidence, then probably the Siege of Sharuhen in 1530 BCE where the Egyptians laid siege to the Hyksos for 3 years. However, it is likely that sieges took place much earlier. Pictographic evidence can be found in the siege fresco from Akrotiri on Santorini. The Cycladic-Minoan town of Akrotiri was buried by the eruption of the Thera volcano between 1650 and 1560 BCE.