Learn English – Are there any English sayings to the effect that little changes may lead to big changes

Wow, that's a useful saying. English seems to have the opposite sayings -- that success or failure of a particular sort make repetitions less likely:

The cat, having sat upon a hot stove lid, will not sit upon a hot stove lid again. But he won't sit upon a cold stove lid, either. -- Mark Twain

or

Lightning never strikes twice in the same place

I'd say something similar would be:

A watched pot never boils

Waiting for something to happen makes it seem like it is happening slower, whereas if you go away and do something else then time will seem to pass faster.