I'm not sure why you think "any one bacterium's mutation must become universal across the globe". That's a pretty strange takeaway in the presence of a mutation that is so advantageous it lets you become a predator and hunt other bacteria or run away from predators and gain a painfully obvious survivability benefit.

The takeaway should be "mutations that confer massive benefits can become universal across the globe even if they only happen once, no matter how unlikely they are", which is obvious and intuitive.

It's more the probabilities, I think[1] - even in one generation, (say) 26 trillion[0] bacterium are going to experience a lot of mutations.

[0] Which is an extremely low ball number for worldwide bacterium, even billions of years ago, I think, given your average human has around 30 trillion inside them.

[1] Like "anomalies in Minecraft" series - given how many seeds there are, how many people play it, and how big the worlds are, eventually even the rarest things generate naturally.

And when you get into things like lateral gene transfer it's not even a tree any longer.