We have a working system. That's why our world's population is so large. And it improved over time, as in more efficient ways to grow food, more productivity, the green revolution, to feed more, then roads/cities/buildings tied to single spots improving efficiency, giving safe housing to billions, mass transport and global logistics.

So what will happen if that gets disrupted? And badly disrupted, while at it. And while that is happening, multiple other things pile up in different ways everywhere?

Thats the danger. You don't die from climate change. You may occasionally die from increasingly frequent extreme weather, a flood because rains, some dam break, extended forest fires and so on. But that is not a single catastrophic event that kill billions. What will kill billions are losing food security in big scale, no safe/climate controlled place to live, violence and wars, widespread diseases and no way to help. In some years to decades millions to billions may die by that combination of factors.

So no, it wont be a single day, sudden event that will kill billions. Is the breakup of the system that holds it together. Agriculture needs a stable climate, megacities need food, the economic system depend on more things, and everything else is packed together. And the first wave of deaths will be just the start.