In his book on Classical Mechanics, Prof. Feynman asserts that it just does. But if this is really what happens (& if the Principle of Least Action is more fundamental than Newton's Laws), then don't we run into some severe problems regarding causality? In Newtonian Mechanics, a particle's position right now is a result of all the forces that acted on it in the past. It's entirely deterministic in the sense that given position & velocity right now, I can predict the future using Newton's laws. But the principle of least action seems to reframe the question by saying that if the particle ends up in some arbitrary position, then it would take a certain path (namely one minimises the action). But that means that the particle already knows where it'll be and it "naturally" takes the path that minimises the action.
Is there any deeper reason for why this is true? In fact principle of least action seems so arbitrary that it's hard to see why it manages to replicate Newton's Equations? If any of you have any insight into this, please share because I just cannot get my head around it.
Note - Please keep in mind, my question is regarding the principle itself, not the equations that result from that principle.