re: How did Hamas turn the narrative so fast?

The Israelis reacted the way Jews have traditionally reacted to threats when they've had power, they tried to annihilate their enemy and in this case explicitly targeted the civilian population in a way that harks back to the old Testament. The problem is that from a Christian perspective, that's not appropriate response. You can't just openly target civilians, but you also can't kill twenty civilians, for example, to kill one Hamas member. And you can't engage in mass reprisals, you can't level a city to teach the enemy a lesson. These are impermissible acts. The Israels were also calling them human animals, rats, and snakes, and said that anyone who didn't flee was a valid target, but at the same time there was nowhere to flee. Then there were the strikes on the aid distributions, the targeting of the hospitals and bakeries, the very liberal rules of engagement resulted in ordinary people just getting shot too, middle of the day, just walking the down the street, and clips of these episodes were shared widely. If Israel had been the weaker party, then this would have been judged differently, but they're much more powerful than the Palestinians.

The Israelis have always been their own worst enemy as far as PR goes. And this isn't the first time they've done this to themselves. Sabra and Shatilla are earlier examples of this.