I think distribution can be seen as a way to model unknown dynamics over infinitesimal amount of time.
There are more than one way to interpret wave function of electron, such as multiverse interpretation, yet I find a better mental model to make sense of it. Imagine the electrons are flushing in and out of control in fractions of seconds. When they flush into existence, their position follow that distribution prescribed by the wave equation. This can perfectly reconcile wave-particle duality since a realization of a electron is just the instance when it is flushed into existence.
statistical mechanics . there is a way to exactly describe interaction of few particles, yet when they are in the billions, that computation get complicated quickly. There is a possibility that as the computational power increases, that would be the norm one day, for now, let us just assume that no such computational power exist. There are still conclusions we can draw despite the lack of computational power, those constraints manifest themselves as macro parameters such as pressure temperature etc.
The image I have in mind is that while there are steps we can model via differential equations, let us imagine during each transition from one step to the next, there are actually a billion steps we can’t model. There are certain dynamics during that 1 billions steps such that an error distribution can be observed while the next step is realized.
Another imagine I have is that the constraint is imposed over the entire episodic trajectory. For instance Texas Heldom. Every step there is a distribution, and the standard derivation of that distribution would get narrower and narrower as the game progresses and more information is revealed. There is a strategy over that structure.