Rigid Bodies simulation
- Bake to Keyframes
- manually adjusted details in Graph Editor
(to synchronize jump on time into hole out)
If you would need more details to RB I can extend answer.
version with Rigid Body simulation only without postpro
- to avoid jumping you need more smooth curvature of Cylinder
- I had to add more colliders (planes) to push ball into Cylinder and two sides colliders to don't let ball fall from Cylinder
- since the animation is slow you can set Collision Margin very low like 0.01 ( in case of cylinder even less 0.001 to keep ball distance from cylinder minimal)
It really depends what whole motion should looks like, because if you need only this simple result of v02, the Hook Modifier (Timaroberts suggestion) will work faster.
If I Baked to Keyframes this simulation and Decimated keyframes to clean up result, animation curve is really simple.
And result is almost the same