To help the people caught in the middle, from both sides, one has to understand the interests of the Israeli government and Hamas. I think the last actions Biden did have the best chance of stopping the war.

Hamas’s interests are a full retreat of Israeli forces and keeping as many hostages. They don’t really care what happens to the general population. The “political” leaders in Qatar also have an interest of staying there. They are also OK with keeping the war going since as time goes by the public opinion turns more and more against Israel. The latter part can be dealt with by not letting Hamas of the hook for what’s going on in Gaza (if you want to say “But no one is saying they’re not to blame!” - yes, but most aren’t stating clearly the ARE to blame. In practical terms, that’s about the same). Also, pressure can be put on Qatar so they can put pressure on the political leadership, as Biden has reportedly done.

The Israeli government is a bit more complex, as it’s a coalition with three “legs” - Netanyahu/Likud, that mainly want to stay in power and nothing else (the war is good for them, since they don’t have to answer for their part in how it started), the far right that want to take over Gaza (and therefor welcome international sanctions, as it “proves” that the whole world hates Israel and therefore the only solution is to disregard what the world thinks), and the ultra orthodox parties that want to keep certain privileges for their voters.

The international arrest warrants, while not desirable on Netanyahu’s part, actually increase his power. He spins them as warrants against “the entire country”. And in fact, right after they were issued Likud rose in the polls.

So what can be done regarding the Israeli government? Well, Netanyahu is playing all sides against the middle, telling everyone different things while trying to change the situation, no matter what the situation actually is, as little as possible (since any change can result in him losing power). Biden, by stating the offer currently on the table came from Israel tore the mask from Netanyahu’s double speak and makes it harder for him to keep the current situation.