No, it doesn't.
Israel's reaction to Oct 7 came pretty damn late. Western protests were caused by Oct 7, by hamas' massacre, NOT by Israel's reaction. Let's face reality here: the biggest massacre of Jews since the holocaust, and WITHIN 2 DAYS masses of people were "protesting", but really muslims were celebrating the Oct 7 genocide with slogans like "gas the Jews", around the world. From Sydney to London, to Washington. More than a month before Israel did anything other than close the border.
The IDF took 12 days to stop the hamas attack, because the IDF did not immediately send forces (aside from 1 helicopter). You see, Iran's hamas attack was never anything more than a distraction, and Iran always meant for hamas to get slaughtered. The places they attacked, look at it on the map ... there's nowhere to go. Before you see anything remotely important there's dozens of kilometers of desert, without barely any shelter, no trees, no rivers, nothing, without any protection for their forces. They were always going to get slaughtered. Israel fortified Ashkelon, which hamas will need to take before anything will happen. Turns out, hamas was stopped halfway through Sderot, on the public square (look at the map to see just how bad a performance that is. They could literally have walked around it, and nothing would have stopped them. They did not. When facing actual forces, not civilians, hamas couldn't defeat a single police office. They attacked the office, the police officers retreated into the square, and every single hamas attacker that made it into the office died there)
The IDF was afraid (I should say preparing) for a real attack from Hezbollah, keeping their options open. The IDF was 100% correct in their assessment that Hezbollah would attack, over land, before any reaction against Gaza happened, in fact before a single day passed. The Hezbollah attack would come through forest, over mountains, where they might hold actual defensible positions, unlike what hamas did. And the hezbollah attack actually might have gotten support from Syria. It didn't, but that was at least vaguely realistic. So the decision to not immediately counterattack hamas was made. And, obviously, now not talked about anymore.
So no, the protest marches in the west occurred before the first move against Gaza.
Here's a timeline of events:
October 7, 2023 — Hamas and allied militants attacked southern Israel, crossing from Gaza and firing rockets. Israel said about 1,200 people were killed and around 250 were taken hostage. There were some Israeli airstrikes during the attack, but nothing more.
October 9, 2023 — Israel announces the border will stay closed for at least 2 months.
October 9, 2023 — Sydney: a pro-Palestinian protest took place outside the Sydney Opera House, just two days after the Hamas attack. There are accusations of the slogan "gas the Jews" shouted, again and again, at the Opera house and in front of the main synagogue of Sydney.
October 14, 2023 — One of the first big Western pro-Palestinian protests after October 7 took place in London, with thousands marching.
October 15, 2023 — Sydney: thousands joined a larger pro-Palestinian rally in Sydney.
October 21, 2023 — A much larger London march drew about 100,000 people, showing the protests had become mass demonstrations in Western capitals.
October 21, 2023 — Sydney: thousands more marched in Sydney again, after police concerns and legal disputes over approval.
October 22–26, 2023 — Israel carried out a series of limited ground raids into Gaza, including overnight operations and what Reuters described as its biggest raid so far on October 26.
October 27–28, 2023 — The IDF moved in to Gaza.