Problem: Gazan civilians are starving and need medical aid, but Hamas can smuggle weapons and seize (and take credit for or use) aid, so Israel and Egypt need to keep the borders closed.
Solution: Keep borders closed, search everything going in, but allow in Israeli-branded food and medical aid...with bombs strapped to the bottoms of the trucks that can be detonated if food or medicine is seized.
As mentioned before, reducing the violence in the long term requires undermining popular support of Hamas, who gain power every time a Gazan civilian dies by Israeli bombing.
If instead of starving people, you sent them medicine and food branded "Given to the people of Gaza by the people of Israel in their struggle against their Hamas terrorist leaders" or something of the like... and create a remote detonation system such that if the food and medical aid are given to the people, the people get food and medicine and are saved, but if Hamas touches the trucks, the trucks blow up, you:
a) get food and medicine to starving people in a manner Israel, not Hamas, gets credit for
b) make it quite clear to people that playing ball with Israel means food and medicine, and playing ball with Hamas means no food and medicine and more bloodshed.
This would not eliminate civilian casualties from starvation, etc, because Hamas would undoubtedly adapt their tactics (bring civilians on truck raids where you have to blow up the trucks anyway, etc), but it would probably reduce them, while also undermining Hamas' support.