If you want to create something like that using individual uniform geometry, the best approach I can think of is to create geo nodes with just a box in them, and then animate them via keyframing their transforms (NOT THE xform SOP!…otherwise that's considering a vertex animation which is no good for UE4).
You'd want to do something like this:
An option could be to create a box in a geo node, copy it according to the Fibonacci sequence, make sure they're named properly, and animate the pieces over time. Then, put together a bit of python to break out all the pieces into their own geo nodes inside a single subnet, automatically scrub the timeline, and keyframe their transforms. If you export that subnet as an FBX and import it into UE4, UE4 will automatically generate the skeleton for you and skip the entire skinning process in Houdini.
My destruction tool has a similar process using a Rigid Body Packed Object DOP node as its input. You could use that as a basis to create another tool that uses any SOP node.https://github.com/sideeffects/GameDevelopmentShelf
If you want to skip the python part, you might be able to animate it at the SOP level, pack the geometry using an assemble SOP, import it into a DOP network via Rigid Body Packed Object DOP, and then use the above tool.
If I get the chance, I'll see about putting a little example together.