The solution to this particular mess in, theoretically at least, straightforward. Like Israel has with the Gulf States, the three sides (Israel, Egypt & Hamas) get talking, under the auspices of a neutral party.
- Hamas agrees to recognise Israel and cease military and other attacks.
- Israel recognises Hamas as the appointed representative of the people of Gaza (I doubt there's any prospect of free and fair elections in the short term).
- Israel & Egypt agree to open the border, maybe under neutral supervision initially, and relax controls.
- Investment from the US, EU, China, India etc is directed to improve the lives of the people of Gaza and make them self-sufficient.
- Arab countries agree to offer citizenship to anyone who doesn't want to remain in Gaza.
- After a period of time, say 5 years, Israel recognises Gaza as an independent state.
But theory and practice are, unfortunately two different things. If Hamas genuinely wanted a free, independent Gaza, they could have had that by now. But their current aim is the destruction of Israel.