How to animate into one object wrapping around another?

I've followed this tutorial to wrap object A around object B using the surface deformer and it worked well:

https://www.youtube.com/watch?v=1mBG9TL6ZU8&ab_channel=SergeStep

My issue is, I want object A to start flat on the ground and to wrap around object B as it rolls over it. So I basically don't want it to deform until a object A comes into contact with it. I tried keyframing the strength but the transition isn't smooth. The object rotates and scales in an odd way.,

Is there a better method for this look?