I added a Vertex Map on the Spline with a Box Field. I am using that Vertex Map in the Spline Emitter to ONLY emit from the parts of the spline that are outside the Box Field.

https://www.dropbox.com/scl/fi/5cofbyyq73l2qbszk10tj/sound_base_ctrl_single-Velocity-Math-Vertex-01A.c4d?rlkey=7oogulihz5io9s5zpyekdnt9n&dl=0

One way is to use a Math Modifier in the Particle Group set to Fields that uses the same Sound Field to Add velocity on the Y Axis

https://www.dropbox.com/scl/fi/mzoawqf2if5mlpwzifbvt/sound_base_ctrl_single-Velocity-Math-01A.c4d?rlkey=1e18dwwdh76jgp84gmyvbpy2e&dl=0

I'm afraid I'm not sure what you want to do.
You don't want emission at 0% sound and want emission at 100% sound. What happens from 1-99%
Some sort of reference video would be helpful... or a series of still frames to show the progression

I don't know if this helps but here's some guidance and a plugin
https://bakedpixels.publixr.com/gltf-export/

You can use the align to spline to move it on a predefined spline, but I assume you want it to appear it's not just moving, but rolling properly. As I mentioned above, this is not as simple as just moving on a spline or a surface.
Are you trying to replicate the instagram animation?

@Kh said

As far as I know, it's a rolling cube animation that was baked into an Alembic, and later the end frame of the Alembic was changed.

You cannot change anything in an alembic. It's all baked. UNLESS the Alembic was only the Rotation Not the movement. That animation has many more details not explained in that answer...
Some cubes stop, wait and then change direction. Some cubes Roll into place while others slide into place.

Not directly. The animation of the Alembic is defining the Position and rotation in your setup.
To achieve that, you would need to just do the rotation and then find another way to move the cubes.
Is there a reason you are using Alembic? Are you planning to replace the cubes with with something else?
As far as the Instagram post, I have no idea how that was done... it's an interesting setup but without some sort of information I need to do a lot of experimentation to figure it out... at the end of the day, would you know if the hand animated every individual cube?...

The key point is that Multi instances will not work in this case. Also you had a Step Effector with a Step field. That will not work.
Here's a setup with a Plain Effector offsetting the animation timing by 20 frames.
The expectation that they will continue moving is incorrect. You can loop the animation but each cube will return to the starting position as the motion is baked in the alembic and Mograph has no idea where each cube is...

Go to the same folder and download "alembic-animation_offset.c4d"

can you also upload the alembic please?

Oh, haha, sorry it's in the Cineversity Forum Folder