Sadly, we’ve been here before: the militant Islamist Hamas movement in Gaza, on Israel’s southern border, firing missiles at Israeli towns and cities, Israel responding with overwhelming force, hundreds of innocent civilian lives lost, mostly Palestinian.

But while the military equation hasn’t changed, the political context has.

A critically important paradox lies at the heart of this latest round of fighting, the third major outbreak in the last dozen years. How it’s resolved will determine what happens when the guns fall silent again.

On the one hand, the fighting has shaken a widespread belief in Israel that the Israeli-Palestinian conflict was fading away, and has put the idea of a “two-state” solution back on the table. On the other, both Hamas and Israeli Prime Minister Benjamin Netanyahu are implacably opposed to any such negotiated compromise.

And both, at least for now, stand to emerge politically strengthened from the latest bloodletting.

Hamas will feel it has achieved what it was seeking last week by targeting missiles not just at nearby southern Israeli towns but also, crucially, at Jerusalem – the disputed holy city at the root of the current conflict, where Israeli police were clashing with protesters angered by the threatened eviction of a number of Palestinian families.

Hamas’ aim? To claim overall Palestinian leadership at a time when the internationally recognized Palestinian Authority on the West Bank has been drained of most of its authority at home and is finding it increasingly difficult to make its voice heard abroad.

For Mr. Netanyahu, Israel’s longest-serving leader, the showdown came at the most precarious point in his political career. Facing trial on corruption charges, he had failed to assemble a new governing coalition after a fourth indecisive election in two years. Rival politicians on left and right were working to form an alternative coalition – including, for the first time ever, a Muslim party representing Arab Israeli citizens.

Within days, the situation for Mr. Netanyahu changed. He was leading a country united by the need to bring an end to the Hamas rocket attacks. Opposition leaders suspended their coalition talks, with all potential partners aware they’d be risking the ire of their own constituents by launching a joint Jewish-Arab government amid the escalating violence.

The key question now will be on the other side of the paradox: whether the short-term political effects of the fighting give way in the months ahead to a renewed focus on trying to find a long-term compromise between Israel and the Palestinians.

That will depend not just on Israelis and Palestinians, but on outside powers such as Arab countries, the European Union, and above all Israel’s principal ally, the United States.

The prognosis: It could happen, but the obstacles are daunting.

First, the fighting has to end. If the template of past Israel-Hamas confrontations holds, that is likely to happen in the coming days: The Israeli military will step up attacks to destroy as many Hamas targets as possible, world pressure will build amid rising civilian casualties in tiny, densely populated Gaza, and Egypt will mediate a truce.

One early sign of the political winds will then come from Israel: Will Mr. Netanyahu’s rivals resume their efforts to form a coalition government, even one including Arab parliamentarians? If not, there is little chance of a parliamentary majority, and a fifth election might be on the way.

If that happens, will the Israeli-Palestinian conflict be a major campaign issue, unlike the last four elections?

A weakened Palestinian Authority would welcome a renewed push for a negotiated compromise, with the prospect of a PA-led state made up of the West Bank and Gaza Strip alongside Israel. So, too, would European countries and much of the international community. They’ve never wavered from their commitment to the two-state formula.

But the critical player will be America. Former President Donald Trump broke with decades of U.S. policy by shunting aside the two-state idea and backing Mr. Netanyahu’s right-wing nationalist coalition in its bid to cement open-ended Israeli control of the West Bank.

The Trump administration also mediated groundbreaking peace deals between Israel and two Gulf Arab states, the United Arab Emirates and Bahrain. Since this required the Arab leaders to ignore protests from the Palestinians, it reinforced the sense for most Israelis that the Palestinian issue was far less pressing than it had been.

President Joe Biden has reaffirmed his support for the two-state model. But his foreign policy focus has been on repairing U.S. alliances and dealing with China, not on the Middle East.

And he has been close enough to the corridors of power for long enough to know only too well how Israeli-Palestinian diplomacy has been bogged down in stalemate since the turn of the century. It has been more than two decades since President Bill Clinton tried, came close, but ultimately failed to bring a two-state deal to fruition.

That may leave Mr. Biden profoundly dubious about embarking on a new U.S. diplomatic push.

Still, the current fighting has raised another question at the heart of the Gaza paradox: whether the price of not doing so might be too high.