Your 'bigger picture' is a fine old mix of distortion, invention and air brushing.
'Islamic countries' didn't co-ordinate in 1967 - they scrambled to respond to an Israeli pre-planned attack. They barely co-ordinated in 1948 or 1973 either.
Why should they 'evacuate' 'fellow Muslims' from Gaza - they should be doing everything possible to stop the war and allow the Palestinians of Gaza to live free and safely in their homes. Are they supposed to evacuate Palestinian Christians and non believers too?
Hamas had a bloody/scheming agenda, but it is dwarfed by the bloody/scheming agenda of the Israeli government and military!
A match was struck on 7 October - clearly - but the fires had been burning (and the corpses and injustices mounting up) for decades.
It is convenient to pretend that history began on 7 October - but it is not true. As the Secretary General of the UN explained (to Israeli outrage) in November - there was a long and bloody backstory of Israeli persecution, expropriation and apartheid before the Hamas attack.