POKROVSK, Ukraine — Camouflaged in a heap of branches cut from nearby trees, the weapon that Ukraine hopes will make a critical difference in its war with Russia is all but invisible from more than a few feet away. Soon, a single round shoots out with a boom and a howling, metallic shriek as it sails toward Russian positions. It is the American-made M777 howitzer. It shoots farther, moves faster and is hidden more easily, and it’s what the Ukrainian military has been waiting for. Three months into the war in Ukraine, the first M777s — the most lethal weapons...