How does a box move uphill

Imagine a scenario where you have a box in a frictionless environment sitting on a parabola, starting high on one side. First gravity pulls the box down and the normal force causes horizontal movement. That's all fine and dandy. But when the ball reaches the bottom and starts moving up again: what generates the force which allows a moving box to travel uphill? It is clearly accelerating in the y-axis, but the net force (I assume (is still pulling the box down).

This is a conceptual question. I can easily figure out how high up a hill a moving object can travel using energy conservation, but my question is, for a force diagram, where is the force being generated that pushes the box up?

My intuition tells me it must be the normal force, but the normal force is proportional to the weight, so it shouldn't allow for positive acceleration in the y-plane.

My second guess is that it must come from the box pushing against the ground as it de-accelerates, but that deaccelation is from the normal force, right? So aren't we back to square one? Normal force is proportional to weight, so the angle of the incline determines how fast we de-accelerate, but then where does the net y-axosnforce come from the allows us to move in the y-direction.

A force diagram would be greatly appreciated.