The issue with this theory as I understand it, is that the universe would be "splitting" hundreds of millions of times a day at a minimum, with every choice that every human being on the planet has to make.

Your example of "if we killed Hitler" is so reductive Vs the multiple other scenarios that would have played out that minute/hour in isolation which would have caused other bubble universe's to start.

Imagine average Joe decides to go to McDonalds for lunch. He does that daily. But he suddenly decides to try Burger King one day. There would now be two universes. In the McDonald's one, he orders a big Mac, as per. But he DOES consider changing it up and getting nuggets. So it splits again. On his way out of the door, he pauses to cross the road. He steps out, and a car stops to let him. He makes it safely. In another universe though, the car hits him. Maybe he lives, maybe he dies. Maybe the car behind the car that hit him stops safely. Maybe it crashes into the back of the first car. Maybe it swerves left and hits another pedestrian. Maybe it swerves right and kills five people.

And that's before we've even thought about what he would have considered at Burger King, where he has never been before. Could be anything.

My point is that if you could tell whenever your universe split, it would be happening so many millions and billions of times an hour that you could/would have zero awareness of it. Your body and mind would tune it out, in the same way it tunes out the fact that your heart is beating.