There's a billiards simulator/game[1] that uses event prediction instead of step-based physics for realistic and reproducible results. It solves the equations of motion to find the next event, animates to that point, and continues until nothing is moving. This is feasible since there are only 16 balls and 1 cue tip, but I imagine that as computational power continues to increase, the scale of such simulations will increase too. I'm excited to see what's next :)

[1] - I read a paper that specifically talked about step-based vs event-prediction for billiards simulation, but I can't find it now :/ Virtual Pool 4 might use the system for its physics, but don't quote me on that!

P.S. - Unity has a pretty handy built-in CharacterController class that lets you move around while respecting collisions -- you just need to add your own Gravity. Also, for more advanced character movement, Catlike Coding has a great series of tutorials: https://catlikecoding.com/unity/tutorials/movement/