It seems to me that Hamas' rocket barrages have tipped a scale they will wish they hadn't. While Hamas lobbing a few missiles every few months could be handled by Israel's Iron Dome missile defense system, lobbing thousands will simply overload those defenses. Once that capability is displayed to Israel's population, I suspect the Israeli leadership has no choice but to make sure this cannot happen again in the future.
I don't believe Israel can simply accede to a cease fire under the current conditions. They will surely be aware that Hamas will simply restock and the next time Israel will be in an even worse situation.
Israel will have no choice but to prevent this situation from continuing. Maybe heavy rocket barrages and embargoes against Hamas in Gaza might suffice. But I doubt the international community will live with that. Israel will have a relatively short term opportunity before their opposition in the international community gets their act together and starts passing UN resolutions. My guess is Biden won't veto anything.
I don't see much of an option except for an invasion of Gaza by Israel. It will last at least as long as it takes them to destroy the missile system infrastructure, and very probably long enough to remove most of the Hamas war making capabilities.
Maybe I'm wrong. Israel might accept a high level of risk and accept a cease fire. There is also the possibility that Hezbollah will get involved and start their own rocket barrages. That would start a regional war. There don't appear to be any good or safe options going forwards for the people in that region.